The Even Number
I am a three-digit number. My three digits are all different, and they multiply to 6. I am even, and I am less than 200. What number am I?
Which three different digits multiply to 6?
132
Different digits that multiply to 6 can only be 1, 2 and 3. Below 200 means starting with 1: 123 or 132. Only 132 is even.
How to solve it
Step one: find the digits. Three different digits must multiply to 6. Zero is out, because any product with 0 is 0. Six splits into whole factors as 1 times 6 or 2 times 3, so as three digits it is 1 times 1 times 6 or 1 times 2 times 3. The first repeats the 1, so the digits must be 1, 2 and 3.
Step two: use the size clue. Less than 200 means the hundreds digit is 1. That leaves only two numbers: 123 and 132.
Step three: use the even clue. An even number ends in 0, 2, 4, 6 or 8. 123 ends in 3, so it is odd. 132 ends in 2, so it is even. Check: 1 times 3 times 2 is 6, all digits differ, 132 is below 200 and even. The answer is 132.
The usual wrong answers are 123, which is the first arrangement people write down but is odd, and 312, which is even but well over 200. Reading every clue before settling on an answer avoids both.
