Minute Mystery: The Three-Digit Number

Bite-sized brain teaser to solve in a minute or less.

 

 

The Three-Digit Number

A teacher writes a three-digit number on the board. The following clues are given:

What is the number?

 

 

Solution

Understanding the clues: Let the three-digit number be represented as abc, with a, b, and c as three separate digits We know that: a + b + c = 12 The digits a, b, and c must all be different The number 100a + 10b + c must be divisible by 7   Search for candidates: We need a three-digit number whose digits sum to 12 Some possible options could have been 3 + 4 + 5 = 12 / 1 + 9 + 2 = 12 / 7 + 4 + 1 = 12. However, these are not divisible by 7 A suitable candidate is 147: Sum of digits: 1 + 4 + 7=12 The digits 1, 4, and 7 are all distinct 147 ÷ 7 = 21, so 147 is divisible by 7 Since 147 meets all the criteria, it is the correct number. The number on the board is 147.