Sides Reversed Is Puzzle - Solution
The Puzzle:
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