Question

Find the smallest distinct positive numbers that provide a counterexample to show the statement is false.

when any number is multiplied by 6 and the digits of the answer are added , the sum will be divisible by 6.

The counterexample is ___.

Answer 1

You coulf d be a genius and instantly see the pattern and answer (I can't), or work out all the possible numbers! Since they want "smallest distinct positive numbers", that would be 1-9:

1 x 6 = 6
6/6 = 1

2 x 6 = 12
(1+2)/6 = 1/2

3 x 6 = 18
(1+8)/6 = 3/2

4 x 6 = 24
(2+4)/6 = 1

.... and so on.

You can that not all final numbers are divisible by 6! Like those that are fractions.