The development of cognitive learning activities in mathematics lessons is an urgent problem in modern primary schools. The article examines the issues of the process of formation of cognitive universal educational actions in younger schoolchildren when solving olympiad assignments. The authors clarify the concept of an Olympiad task, highlight characteristics olympiad assignments and provide olympiad assignments that can be used when studying individual course topics to form cognitive universal learning activities in mathematics lessons. The authors come to the conclusion that the use of Olympiad tasks in mathematics lessons ensures high motivation of students and their interest in the subject, contributes to the formation of cognitive universal educational actions, and, as a result, the assimilation of a knowledge system and the formation core competence- “ability to learn.”
Olympiad tasks
cognitive universal educational activities.
1. Asmolov A.G. How to design universal learning activities. From action to thought: a manual for teachers / Ed. A.G. Asmolov. – Ed. 2nd – M.: Education, 2010. – 152 p.
2. Drozina V.V. Features of teaching junior schoolchildren to solve non-standard problems (olympiad) problems. 2010. No. 11.
3. Istomina N.B. Methods of teaching mathematics in primary school/ N.B. Istomina - M.: Publishing house. Center "Academy", 1999. - 288 p.
4. Sample programs in academic subjects. Elementary School. M.: Education, 2010. P. 399.
5. Dictionary Russian language. http://www.vedu.ru/expdic/20048/
6. Friedman L.M. Plot problems in mathematics. History, theory and methodology. M., 2002.
Primary general education is intended to lay the foundation for achieving the strategic goals of subsequent stages of human education (self-education). This is exactly the strategy, taking into account many years of positive experience national school in the field of pedagogy, implemented in the new Federal state standard primary general education. The priority of primary general education is the formation of universal educational activities, the level of formation of which largely determines the success of all subsequent education. The goal of school education is to develop in students the ability to independently set educational goals, design ways to implement them, monitor and evaluate their achievements, in other words, the formation of the “ability to learn.” The concept of the development of universal educational actions was developed on the basis of the activity approach (L.S. Vygotsky, A.N. Leontiev, P.Ya. Galperin, D.B. Elkonin, V.V. Davydov, A.G. Asmolov) by a group of authors: A.G. Asmolov, G.V. Burmenskaya, I.A. Volodarskaya, O.A. Karabanova, N.G. Salmina, S.V. Molchanov and others.
The development of cognitive universal learning activities in mathematics lessons is an urgent problem in modern primary schools. The Federal State Educational Standard for Primary General Education describes the requirements for the results of mastering the basic educational program primary general education. The standard establishes requirements for the results of students who have mastered the basic educational program of primary general education: meta-subject, including universal learning activities mastered by students (cognitive, regulatory and communicative), ensuring mastery of key competencies that form the basis of the ability to learn, and interdisciplinary concepts.
Olympiad tasks included in the context of a mathematics lesson will help students achieve their planned results. But younger schoolchildren often have difficulty solving them. The reasons for this situation, in our opinion, lie in the lack of a systematic approach to teaching how to solve this type of task. In this regard, we decided to describe the possibilities of developing in mathematics lessons in the 3rd grade various types cognitive universal educational activities through the inclusion of olympiad tasks in the lesson content.
Before starting work, we found out which tasks can be called Olympiad. A task is something that is assigned to be completed, an assignment. The Olympics are competitions, competitions - sports, artistic or in the field of some knowledge. V.V. Drozina compares the concepts of “olympiad problem” and “non-standard problem”. By a non-standard task, she understands a task that contains something original and creative. According to the definition of L.M. Friedman, standard problems are those for solving in school course Mathematicians have ready-made rules or these rules directly follow from any definitions and theorems that define a program for solving these problems in the form of a sequence of steps.
Based on this definition, we have clarified the concept of “olympiad task” - this is a task for which there is no general rules and provisions defining the exact program for its solution.
There is no standard algorithm for solving Olympiad tasks. Each such task is unique and requires the use of new ideas to answer the question posed. But there is no need to obtain special knowledge, since the knowledge acquired within the framework of the primary school program is sufficient to solve the Olympiad tasks.
Let us highlight the characteristic features of the Olympiad tasks:
1) the implementation of such a task entails direct development;
2) the task may use non-standard forms and methods of presenting data;
3) fictitious or real objects (characters) are used in the form of initial data, using which you can achieve your goals;
4) this can be a qualitative problem, the solution of which is constructed using a logical chain of reasoning and does not require performing mathematical calculations;
5) the task may contain an unusual or non-standard question.
In the classroom, it is advisable to use Olympiad tasks that can contribute to the development of cognitive universal learning activities. The rational use of tasks of this type is ensured by their connection with the program material.
The following tasks can be included in the content of mathematics lessons when studying the topic “Motion Problems”.
Let's give examples of such tasks.
1. The distance between two cyclists moving on the road is 20 km. Cyclist speeds are 8 km/h and 10 km/h. What could be the distance between them after an hour?
2. Two motorcyclists rode towards each other from two villages, the distance between which is 355 km. The speed of the first motorcyclist is 10 m/s, and the speed of the second is 25 m/s. After what time will the distance between motorcyclists be 85 km?
3. Kolya drew 4 straight lines. On each of them he marked 3 points. In total he got 7 points. How did he do it?
4. Ivan Tsarevich, leaving city A, saw 3 roads leading to city B. After thinking a little, he drove along one of them. Leaving city B, Ivan saw two roads leading to city C, and one road that led to city D. Arrived at city C. Leaving it, he saw three roads leading to city D. How many different options fairy tale hero could you travel from city A to city D without returning?
5. Masha was given a new bicycle, and she tries to take care of it, sometimes she rides, and sometimes she walks, and carries the bicycle next to her. On Monday Masha went to her grandmother on foot, and Return trip I rode a bicycle, spending 60 minutes the whole way. On Tuesday, Masha rode a bicycle to her grandmother and back and was on the road for 30 minutes. On Wednesday, Masha decided to visit her grandmother and took a walk there and back. How much time will Masha spend on this walk?
6. The dog ran 100 m in 14 seconds. Will she be able to run 2 km in 4 minutes if she runs at the same speed?
7. A motorcyclist left the village for the city at a speed of 24 km/h. At the same time, a cyclist left the city for the village at a speed of 8 km/h. Which of them will be further from the village after 2 hours of driving, if the distance between the city and the village is 64 km?
The following tasks can be included in the context of lessons on the topics “Numbers from 1 to 1000”, “Arithmetic Operations”, “Problem Solving”.
1. Give the safe code if it is the smallest five-digit number written in different digits.
2. Decipher the rebus: TROUBLE + FOOD + YES + A = 8888 (Different letters indicate different numbers, and the same letters indicate the same numbers).
3. On the door of the treasure cave there is a combination lock with a code. You need to dial seven different numbers on the lock (1, 2, 3, 4, 5, 6, 7, 8, 9) so that the numbers do not repeat and the equations are correct.
4. What integers, not exceeding 1000, are equal to the number of letters if they are written in letters in Russian? (Please list all options.)
5. Find natural numbers whose sum is 20 and whose product is 420.
6. Place action signs and brackets between some numbers so that equalities are obtained. 1 2 3 4 5 6=1.
7. How many two-digit numbers are there in which the second digit is greater than the first?
8. What 5 digits need to be removed from the number 49827640986 to get the number as large as possible?
9. 160 is obtained if you add the minuend, subtrahend and difference. The minuend is greater than the difference by 34. Find the difference, the minuend and the subtrahend.
10. Each of the four boxes contains fruits: apples, oranges, pears, bananas. Each box has a tag, but none of them are correct. Indicate the names of the fruits that are in the boxes.
11. 29 students came to the lesson. 12 of them have a compass, and 18 have a ruler. Three students did not bring either a compass or a ruler. How many students have both a compass and a ruler?
12. The master calculated that he would lay the square floor in the bathroom with square tiles. And he won't have to cut a single tile. First, he laid the tiles along the edges of the bathroom in one row, for this he needed 60 tiles. Calculate how many tiles a master will need to lay out the entire floor?
13. Vitya lives on the sixth floor of the house, and Masha lives on the second. How many times is Vitya’s path longer than Masha’s path if the children started moving up the stairs?
14. The guys are playing football in the yard. Lida, Kolya, Zoya and Misha are sitting on the bench. Zoya sits next to Lida, but not next to Misha. Misha does not sit next to Kolya. Who is sitting next to Kolya?
15. Katya gave Valya half of her sweets and one more. After that, Katya had no candy left. How many sweets did Katya have?
16. Establish a pattern according to which a series of numbers is composed, and continue it with three more numbers: 2, 5, 11, 23, 47...
In mathematics lessons in primary school When studying topics related to the composition of numbers, the numbering of numbers, the formation of cognitive universal educational actions occurs, such as constructing a logical chain of reasoning, putting forward hypotheses and their justification. In these lessons, we consider it appropriate to use Olympiad tasks.
The use of Olympiad tasks in mathematics lessons ensures high motivation of students and their interest in the subject, contributes to the formation of cognitive universal learning activities and, as a result, the assimilation of a knowledge system and the formation of a key competence - “the ability to learn.”
Reviewers:
Litvinenko N.V., Doctor of Psychology, Professor, Head of the Department of Pedagogy of Preschool and Primary Education, Federal State Budgetary Educational Institution "Orenburg State Pedagogical University", Orenburg;
Rusakova T.G., Doctor of Pedagogical Sciences, Professor, Head. Department of Artistic and Aesthetic Education, Federal State Budgetary Educational Institution "Orenburg State Pedagogical University", Orenburg.
Bibliographic link
Mendygalieva A.K., Popova L.N. FORMATION OF COGNITIVE UNIVERSAL LEARNING ACTIONS (BASED ON THE EXAMPLE OF OLYMPIAD TASKS IN MATHEMATICS) // Contemporary issues science and education. – 2015. – No. 4.;URL: http://science-education.ru/ru/article/view?id=20592 (access date: 12/25/2019). We bring to your attention magazines published by the publishing house "Academy of Natural Sciences"
In modern Russian society, which is at the stage of economic and social change, it has become necessary to improve the educational process to improve the quality of education in primary school and the comprehensive development of the personality of a child who is ready to live in a modern information society, independently obtain the knowledge he needs, analyze, synthesize, classify it and use it in a variety of activities. IN market conditions Today, the problem of self-development and self-improvement of the individual through the active and conscious appropriation of new social experience is relevant; the ability to apply knowledge in practical activities. Thus, the need arose for a qualitative restructuring of education: the introduction of new federal state educational standards primary general education (2012), basic acting force which is a system-activity approach to teaching, developing the focus of primary general education and the development of universal educational activities.
In a broad sense, the term “universal learning activities” means the ability to learn, i.e. the subject's ability for self-development and self-improvement through the conscious and active appropriation of new social experience. Universal educational activities are divided into four blocks: personal, regulatory, communicative, cognitive.
Development of cognitive universal learning activities junior school student - the most important task modern primary education. Great opportunities in the field of cognitive development universal actions In mathematics lessons there may be Olympiad tasks. Our research showed that teachers do not always use these tasks in the context of mathematics lessons.
In domestic pedagogical science studying issues related to students’ implementation educational activities, led by leading teachers and psychologists: L. I. Bozhovich, A. A. Lyublinskaya, M. I. Makhmutov, N. F. Talyzina. Their research proves that one of the main reasons for school failure is students' inability to study; Yu. K. Babansky and I. Ya. Lerner note the lack of interest in learning among children, which is explained by the inability to organize their educational work rationally and technologically competently. L. M. Friedman states the relationship between the quality of subject study and the ability of students to learn independently. A.K. Markova, I.I. Ilyasov, V.Ya. Lyaudis identify the components of the “ability to learn” content. IN Lately Special attention of teachers and psychologists is paid to the development of universal educational activities.
IN dissertation research recent years the issues of the formation of certain types of universal educational actions of a junior schoolchild were considered (regulatory - O. V. Kuznetsova, communicative - S. A. Nikishova, cognitive - N. V. Shigapova), the formation of universal educational actions in assessment activities (I. E. Syusyukina) , formation of UUD on individual academic subjects(V. A. Shabanova, D. D. Kechkin), issues of teacher readiness for the development of universal educational actions (A. N. Artemova). The issues of forming universal educational actions for students of basic and high school(E. A. Pustovit, N. N. Solodukhina, A. M. Sukovykh, N. V. Zhulkova, S. V. Chopova, D. A. Koryagin, E. S. Kvitko, S. A. Tyurikova, D. . A. Khomyakova).
E. I. Bezrukova defines cognitive universal educational actions as a system of ways of knowing the world around us, the construction of an independent process of search, research and a set of operations for processing, systematizing, generalizing and using the information received. Under cognitive universal educational actions L.I. Bozhenkova understands actions that ensure the process of cognition, the creative mental process of obtaining and updating knowledge. Cognition in psychology is considered as the ability for mental perception and processing of information. New knowledge is the result of the process of cognition.
I. A. Lebedeva, S. B. Ronginskaya consider the cognitive universal educational actions of a primary school student as “a set of qualitatively different universal educational actions that are in complex and dynamic relationships with each other, united by a common goal of activity. Cognitive actions provide the ability to understand the world around us: the readiness to carry out a directed search, processing and use of information. Cognitive UUDs include: general educational, logical, actions of posing and solving problems, which consist of private skills.
We understand by cognitive universal educational actions such methods of action that contribute to the organization of effective cognitive process ensuring the acquisition, transformation and use of new knowledge. Formation and subsequent development of universal educational actions of the student primary classes is one of the important conditions for successful learning.
Analysis of the concept of universal educational actions allows us to say that elementary education is aimed at the formation and subsequent development of the student’s universal educational actions. Mathematics lessons create the opportunity to organize various types of activities, including olympiad tasks, which contribute to the effective development of cognitive universal educational activities. As a result of considering cognitive universal educational actions, we can conclude that they provide:
Personal development of a primary school student: implementation creativity and self-realization, readiness for independent action;
Student cognitive development: development mental activity, the ability to determine, correct, manage and obtain positive results in the process of cognitive activity;
Communicative development of a primary school student: active interaction with others: with classmates, teachers, peers and adults;
Social development of the student: the increase in new experience in the field of social norms, roles and rules that are new to him.
Teaching younger schoolchildren to solve Olympiad tasks is a condition for the development of cognitive universal educational activities, and also establishes a connection between the process of solving Olympiad tasks and the process creative activity.
The process of developing cognitive universal educational actions in mathematics lessons in primary school takes place in three stages: execution according to a model containing a method of action (“Representation”), implementation of a method of action according to its name (“Method”), application of the necessary method of action in the context educational task(“Mastering UUD”). Developing cognitive universal learning activities means transferring them to the student for use various ways actions at the cognitive level. For this purpose, specially selected Olympiad tasks are used in lessons. The process of developing cognitive universal educational actions in mathematics lessons can also occur through solving problem tasks during the lesson, including olympiad ones, causing the formulation problematic issues and as a consequence of difficulties in solving. But it is the resolution of these difficulties that determines the development process. The choice of a way out of a difficulty depends on the stage of development of cognitive universal educational actions.
We described the levels of development of the action of posing and solving a problem according to selected criteria (motivational, cognitive-activity (practical), volitional. They are presented in Table 1.
Table 1
Level characteristics of the action of posing and solving a problem in younger schoolchildren
|
Criteria |
Low level |
Average level |
High level |
|
Motivational |
The presence of external motives (to achieve praise, to show one’s skills), the teacher’s help is expressed. |
The presence of stable internal motives: to learn something new, to find a way to solve a problem. The younger student realizes that knowledge is necessary to solve it and that new ways of applying it need to be found. However, the help of a teacher is still needed. |
Stable cognitive need and motivation, well-expressed social motives (activity in working with classmates, teachers, librarians). The student receives satisfaction from the results of his own activities. |
|
Cognitive-activity (practical) |
Work according to a model predominates, with the help of instructions, independent actions are inaccurate and uncertain, |
The student independently builds his own hypotheses and actions to find a solution to the problem, and is capable of creativity. |
The younger student is purposeful and variable in his own actions, able to correct the solution to the problem, |
|
elements of creative activity are rarely present. Most often, a junior student achieves results only with the help of a teacher. |
But he is only able to take into account independent reasoning and is not ready to find his own mistakes and make adjustments to the decision. Doesn't always achieve results on his own. |
restore the correct way to solve it, is able to take into account the opinions of others. Problem solving is creative and exploratory in nature. |
|
|
Willpower and self-control are either absent or present extremely rarely, when reminded by adults. |
The student demonstrates sustained volitional efforts, shows responsibility for the results of his own work, but does not see value in collective work |
There is an easy overcoming of difficulties, attentiveness, concentration, responsibility for the results obtained both independently and in a team. A readiness for independent and mutual control is demonstrated. Volitional actions are stable |
Let's consider olympiad tasks in mathematics that contribute to the development of cognitive universal learning activities of a primary school student.
Movement tasks:
The distance between two cyclists moving on the road is 40 km. Cyclist speeds are 10 km/h and 12 km/h. What could be the distance between them after an hour?
Two motorcyclists rode towards each other from two villages, the distance between which was 355 km. The speed of the first motorcyclist is 10 m/s, and the speed of the second is 25 m/s. After what time will the distance between motorcyclists be 85 km?
Kolya drew 4 straight lines. On each of them he marked 3 points. In total he got 7 points. How did he do it?
Ivan Tsarevich, leaving city A, saw 3 roads leading to city B. After thinking a little, he drove along one of them. Leaving city B, Ivan saw two roads leading to city C and one road that led to city D. He arrived in city C. Leaving it, he saw three roads leading to city D. How many different options could a fairy-tale hero get from city A to city D without returning?
Masha was given a new bicycle, and she tries to take care of it, sometimes she rides, and sometimes she walks, and carries the bicycle next to her. On Monday, Masha went to her grandmother on foot, and rode a bicycle back, spending 60 minutes on the entire journey. On Tuesday, Masha rode a bicycle to her grandmother and back and was on the road for 30 minutes. On Wednesday, Masha decided to visit her grandmother and took a walk there and back. How much time will Masha spend on this walk?
The dog ran 100 m in 14 seconds. Will she be able to run 2 km in 4 minutes if she runs at the same speed?
A motorcyclist left the village for the city at a speed of 24 km/h. At the same time, a cyclist left the city for the village at a speed of 8 km/h. Which of them will be further from the village after two hours of driving, if the distance between the city and the village is 64 km?
Problems with numbers and operations on them:
Give the safe code if it is the smallest five-digit number written in different digits.
Decipher the rebus: TROUBLE + FOOD + YES + A = 8888 (Different letters indicate different numbers, and the same letters indicate the same numbers).
On the door of the treasure cave there is a combination lock with a cipher. You need to dial seven different numbers on the lock (1, 2, 3, 4, 5, 6, 7, 8, 9) so that the numbers do not repeat and the equations are correct.
What natural numbers not exceeding 1000 are equal to the number of letters if they are written in letters in Russian? (Please list all options.)
Find natural numbers whose sum is 20 and whose product is 420.
Place action signs and parentheses between some numbers to create equalities. 1 2 3 4 5 6 =1.
How many two-digit numbers are there in which the second digit is greater than the first?
What 5 digits need to be removed from the number 49827640986 to make the number as large as possible?
You get 160 if you add the minuend, subtrahend and difference. The minuend is greater than the difference by 34. Find the difference, the minuend and the subtrahend.
Each of the four boxes contains fruits: apples, oranges, pears, bananas. Each box has a tag, but not one of them corresponds to reality. Indicate the names of the fruits that are in the boxes.
29 students came to the lesson. 12 of them have a compass, and 18 have a ruler. Three students did not bring either a compass or a ruler. How many students have both a compass and a ruler?
The guys are playing football in the yard. Lida, Kolya, Zoya and Misha are sitting on the bench. Zoya sits next to Lida, but not next to Misha. Misha does not sit next to Kolya. Who is sitting next to Kolya?
Katya gave Valya half of her sweets and one more. After that, Katya had no candy left. How many sweets did Katya have?
Establish a pattern according to which a series of numbers is composed, and continue it with three more numbers: 2, 5, 11, 23, 47...
The use of Olympiad assignments in mathematics lessons ensures high motivation of students and their interest in the subject, promotes the formation of cognitive universal learning activities, and, as a result, the assimilation of a knowledge system, the formation of a key competence - “the ability to learn”.
Thus, learning to solve Olympiad tasks in mathematics lessons ensures high motivation of students and their interest in the subject, contributes to the formation of cognitive universal educational actions, and, as a result, the assimilation of a knowledge system and the formation of their ability to learn.
Sheet with Rebuses (first version, will be supplemented)
1) YES + YES + YES = FOOD
2) CAT + CAT + CAT = DOG
3) KICK + KICK = FIGHT
4) SPORT + SPORT = CROSS
5) CAR + CAR = TRAIN
principle - from simple to complex
1)
YES + YES + YES = FOOD
This is the simplest example, I'll put it first
Reasoning from Dema
digit A can only be either 0 or 5
let A=0
then D = 5, therefore E = 1
if A=5
then in the sum of three identical digits, the last digit in the final number must be one less than the same digit (5+5+5 = 15, and the unit is transferred and added to the tens)
Dema did not find such a figure (2*3=6 3*3=9 4*3=12 5*3=15 6*3=18 7*3=21 8*3=24 9*3=27 and 0)
and settled on option 1 as the only correct one.
Addition: The thought that came to my mind after looking at the example with BB (from the entry above) and which I advised my son to write in a column.
The options are becoming clearer.
Reasoning from me:
I see more options for solving the rebus.
For example, on both the left and right we subtract YES
we get YES + YES = E00 (the last digits are two zeros)
the maximum two-digit number 99 gives a total of less than 200,
means E00 = 100
100:2= 50
we get 50+50=100
D=5
A=0
E=1
50+50+50=150
2)
CAT + CAT + CAT = DOG
I set this problem second because you can consolidate the experience gained in the first example
A+A+A=A
the problem has two very similar solutions :)
3)
KICK + KICK = FIGHT
This problem was pulled out from Potapova’s solution book (Arithmetic 5), p. 25
Reflections from Potapov
The sum of four-digit numbers is five-digit, therefore, D = 1, and D + D = 2, but then A is either 2 or 3. Since the number P + P = 2P ends in A, then A is divisible by 2, therefore, A = 2 .
Then P = 6 (so that the total is 12, because 1 is already occupied by D),
U126
U126
_____
162K2
then K=5, Y=8 (total 16)
8126
+8126
____
16252
4)
SPORT + SPORT = CROSS
Reasoning from me
SPORT
SPORT
_____
CROSS
T+T=C, which means C is an even number or 0
C+C=K, which means C is less than 5 and not 0 (a number cannot start at 0)
output: C (even and less than 5) or 2 or 4.
We check both options (C=2 and C=4).
let C=4
and P+P=C (T+T also = C), which means the amount is for a ten (and the second digit 4) = 14
that means... and so on
By the way, at one stage we discover that O is not 0)))
O+O must add up to a number ending with itself minus 1.
О=9 (9+9=18)
We complete the solution and check the second option.
and choose the only correct one.
5)
CAR + CAR = TRAIN
I chose this task because it can be used to consolidate the experience of the previous one. And take a small step forward.
RAILWAY CARRIAGE
+COACH
_______
COMPOUND
Beginning of the reflection:
C=1
H+H=B, which means B is even or 0
the number cannot start with 0, which means B is not 0
and so on
If these problems can be solved easier or in a different way... Or, God forbid, they were solved incorrectly - please let me know. And I will be happy to improve the leaflet.
P.S. in the comments - a useful introductory part
06/05/2011 18:01:01, ABDDavidoffThe topic of puzzles is usually not given with → The topic of puzzles is usually not given with theoretical material.
And I would suggest for restless children - a foundation, the first steps. And then the rebus will be clearer and more attractive for them.
1. ANOTHER DISCHARGE
In case of summation and the appearance of a new digit
if the sum of two single-digit numbers is greater by a sign, then it will be 1
xxx + xxx = Ahhh
A=1
even if we take the most big number(take any number of characters) -
9999+9999=19998
And always equals 1
and never 2, 3 or more
For example,
CAR + CAR = TRAIN
C is always 1
2. when adding two numbers in the ones place, you always get an even number
and the last digit will always be an even number or 0
С+С=2С (even)
1+1=2, 2+2=4, 3+3=6, 4+4=8, 5+5=10, 6+6=12, 7+7=14, 8+8=16, 9+9=18, 0+0=0
from here -
PART + PART = PRODUCT
I=1, and E is an even digit or 0
3. if two identical digits add up to a number whose last digit you know
For example,
L+L=.8
then L - can only be 4 or 9
You can ask your child how to get the number 6?
Answer: 3+3 or 8+8
xxxA+xxxA=xxx6
That
A or 3 or 8
and we can solve the example together
ONE+ONE=MANY
1. what is M equal to? Why?
M=1
2. Since the sum of two O exceeded ten Mx,
means O is greater than 4
Since H+H = o, it means O-even or 0
we ask the child - O is greater than 4 and even,
means O - what is the number...
O or 6 or 8
3. suppose O=6
there are as many as four O in the beginning, we arrange them
and continue to solve the puzzle
So N or 3 or 8 (3+3=6, 8+8=16)
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