NCERT Solution for Playing with Numbers

For the to happen, A must be 7

(∴ A + 5 = 7 + 5 = 12).

So for the addition in tens column, we have

1 + 3 + 2 = B ⇒ B = 6

So, the puzzle has been decoded as

∴ The possible values of A and B are 7 and 6 respectively.

i.e., from A + 8 we get 3, i.e., the number whose ones digit is 3.

For this to happen, A must be 5

(∴ A + 8 = 5 + 8 = 13)

So for the addition in tens column, we have

1 + 4 + 9 = B ⇒ 14 = B

∴ Clearly, B is 4 and C is 1.

So the puzzle has been decoded as

∴ The possible values of A, B and C are 5, 4 and 1 respectively.

A and B.

Study the addition in the given puzzle.

i.e., from B + 7 we get A and from A + 3 we get 6. Possible values can be

0 + 7 = 7 i.e., A = 7 but 7 + 3 ≠ 6, so rejected

1 + 7 = 8 i.e., A = 8 but 8 + 3 ≠ 6, so rejected

2 + 7 = 9 i.e., A = 9 but 9 + 3 ≠ 6, so rejected

3 + 7 = 10 i.e., A = 0 but 1+ 0 + 3 ≠ 6, so rejected

4 + 7 = 11 i.e., A = 1 but 1 + 1 + 3 ≠ 6, so rejected

5 + 7 = 12 i.e., A = 1 but 1+ 2 + 3 ≠ 6,

So, this value of B = 5 works out correctly and B = 5 gives A as 2. So, the puzzle has been decoded as

A and B.

Study the addition in the tens column : from 2 + A we get 0, that is, a number whose ones digit is 0. For this to happen, the ones digit of A should be 8. And since A is a digit, we get A = 8. So, the puzzle becomes

Now, study the addition in the ones column : from 8 + B we get 9. For this to happen, we must have B = 1. Therefore, the puzzle has been decoded as