# Sides Reversed Is Puzzle - Solution

### The Puzzle:

Hungry Horace was copying down his Mathematics Homework the other day, but because he was in a rush (he wanted to be first in the dinner queue) he copied it down incorrectly.

They had been learning about multiplying 2 digit numbers, and had five questions to do at home. Horace, however, copied every number down backwards:

Instead of writing 12 x 42 Horace wrote 21 x 24

Instead of writing 12 x 84 Horace wrote 21 x 48

Fortunately for Horace, all his answers were still correct!

What were the other three questions?

They had been learning about multiplying 2 digit numbers, and had five questions to do at home. Horace, however, copied every number down backwards:

Instead of writing 12 x 42 Horace wrote 21 x 24

Instead of writing 12 x 84 Horace wrote 21 x 48

Fortunately for Horace, all his answers were still correct!

What were the other three questions?

### Our Solution:

Instead of writing 12 x 42, Horace wrote 21 x 24

Both give the answer 504 because 1 x 4 is the same as 2 x 2.

Instead of writing 12 x 84, Horace wrote 21 x 48

Both give the answer 1008 because 1 x 8 is the same as 2 x 4.

We also know that

1 x 8 is the same as 4 x 2,

1 x 6 is the same as 3 x 2,

and 1 x 6 is the same as 2 x 3.

So the other three questions were 14 x 82, 13 x 62 and 12 x 63.

Both give the answer 504 because 1 x 4 is the same as 2 x 2.

Instead of writing 12 x 84, Horace wrote 21 x 48

Both give the answer 1008 because 1 x 8 is the same as 2 x 4.

We also know that

1 x 8 is the same as 4 x 2,

1 x 6 is the same as 3 x 2,

and 1 x 6 is the same as 2 x 3.

So the other three questions were 14 x 82, 13 x 62 and 12 x 63.

Puzzle Author: Stephen Froggatt

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