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NCERT Solutions for Class 4th Maths Chapter 10 How to play and who wins — NIM Game (2 Player Game)

Book page 149 Updated on2026-09-19

Q1.
Can you win the game if the other player has reached the total of 6 and it is your turn?
Answer

Yes. You can win for sure.

Total now = 6
You add 1 → total 7
Now the other player can only make 8 or 9
From 8 you add 2 → 10
From 9 you add 1 → 10

Either way you reach 10 first, so you win.

Why it happens: 7 is a safe number. From 7 the other player can never touch 10, but you always can.
Tip: The safe numbers in this game are 1, 4, 7. Try to say them.
Q2.
Can you win the game if the other player has reached the total of 7 and it is your turn?
Answer

No. Here the other player wins.

Total now = 7. You need 3 more, but you may add only 1 or 2.
If you add 1 → total 8, and the other player adds 2 → 10
If you add 2 → total 9, and the other player adds 1 → 10

Whatever you do, the other player reaches 10 first and wins.

Why it happens: 7 is a safe number. It is 3 away from 10, and 3 is too big for one move, so the player who must move from 7 always loses.
Tip: Try to be the one who says 7. Then you are safe.
Q3.
Can you win the game if the other player has reached the total of 8 and it is your turn?
Answer

Yes. You win in one move.

Total now = 8
8 + 2 = 10

You add 2 and reach 10, so you win.

Why it happens: 10 is only 2 away from 8, and 2 is a move you are allowed to make.
Check it yourself: From 9 you also win, because 9 + 1 = 10.
Q4.
Play the game to reach other target numbers (like 10, 11, or 12) by adding 1 or 2 each time. Can you find a number in each case when you are sure that you can win?
Answer

Yes. Count back from the target in threes.

TargetSafe numbers to say
101, 4, 7
112, 5, 8
123, 6, 9

If you say a safe number, you will surely win.

Why it happens: Each round the two players together add 1 + 2 = 3, or 2 + 1 = 3. So the safe numbers go down in steps of 3 from the target.
Try This: For target 12, say 9. Then the other player must make 10 or 11, and you finish at 12.
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