Zachery, Shelley and Kelly are three friends. One of them is 9 years old, one is 10 years old and one is 11 years old.

They asked their teacher to guess their ages. The teacher said: “Zachery is aged 9. Shelley is not aged 9. Kelly is not aged 11.”

Only one of the teacher’s statements is correct. How old are Zachery, Shelley and Kelly?

Under 20 Age 10-14

I divided one whole number by another.

Each of them was less than 20.

The answer on my calculator was 0.5384615.

What were the two numbers?

Guess my age

Zachery is 11, Shelley is 9 and Kelly is 10.

Assume the first statement is true, so Zachery is 9. The second statement is then not true, so Shelley is 9, which is impossible.

Assume the second statement is true, so Shelley is 10 or 11. Zachery is then 10 or 11, and Kelly is 11. These cannot all be true.

Assume that the third is true, so Kelly is 9 or 10, Zachery is 10 or 11, and Shelley is 9. So Kelly is 10 and Zachery is 11.

Under 20

The numbers were 7 and 13.