The Two Digit Number Puzzle

Question :

You have to find a two-digit number that meets the following criteria:

The number is a multiple of 3.

The sum of its digits is 7.

Can you find the number?

Solution:

Let's break down the criteria:

The number is a multiple of 3: This means the number could be 12, 15, 18, 21, 24, ..., 99.

The sum of its digits is 7: The sum of the digits must be 7, so the possible pairs of digits are (1, 6), (2, 5), and (3, 4).

Now, let's find a number that satisfies both conditions:

For the pair (1, 6), the number is 16. However, 16 is not a multiple of 3.

For the pair (2, 5), the number is 25. 25 is not a multiple of 3.

For the pair (3, 4), the number is 34. 34 is not a multiple of 3.

We need to keep searching.

For the pair (4, 3), the number is 43. 43 is not a multiple of 3.

For the pair (5, 2), the number is 52. 52 is not a multiple of 3.

For the pair (6, 1), the number is 61. 61 is not a multiple of 3.

Continuing...

For the pair (7, 0), the number is 70. 70 is not a multiple of 3.

For the pair (8, -1), the number is 81. 81 is not a multiple of 3.

For the pair (9, -2), the number is 92. 92 is not a multiple of 3.

The only pair we haven't tried yet is (8, -1), but it doesn't form a valid two-digit number.

It seems like there's no two-digit number that satisfies both conditions. But wait! We forgot about zero!

For the pair (0, 7), the number is 07 (which is equivalent to 7). 7 is a multiple of 3 and has a digit sum of 7.

So, the two-digit number that meets all the criteria is 07.

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