To Whom It May Concern

I'm a 37 year old mother and i have returned to school for personal reasons. I was faced with this question.
Choose any number less than 10, multiply it by 8547, then take your answer and multiply it by 13. I chose the number 8.

8547
 x 8
--------
68376

and

68376
 x 13
---------
205128
68376
---------
888888

Any number chosen from 1 to 9 will result in the same form of answer.If the number two is used you will end up with 222,222.etc So my question is, is there another number that will results in the answers.

Hi Brenda,
This is a cute trick.

Since multiplying three numbers in any order gives the same result, you can start by multiplying 8547 by 13 and then multiply the result by 8. But 8547 times 13 is 111111 and obviously 111111 times 8 is 888888. Now you can see why 8547 times 2 times 13 is 222222 since 8547 times 13 is 111111 and 111111 times 2 is 222222.

To find other numbers that give the same result you need two numbers that have a product of 111111. Since 3003 times 37 is 111111 you can perform the same trick as follows.

Choose any number less than 10, multiply it by 3003, then take your answer and multiply it by 37. The result will be the same as with 8547 and 13.

Can you find two other numbers that will also work?

Cheers
Harley