- 3

- 0

## Main Question or Discussion Point

Find all positive integers n (n will be called special)

such that if n divides a three digit number say ABC where A = hundreds, B = tens, C = ones. Then n also divides BCA and CAB.

So far I have worked out that 1 is special of course, so is 3 (factor test sum of digits will always be the same) and 9 as well as 111,222,333....999 and any number greater than 1000 as it will only divide into the 3 digit number 000.

Also worked out: n cannot be:

n - divides this - not this

2 - 132 - 321

4 - 492 - 249

5 - 335 - 353

6 - 336 - 363

7 - 861 - 618

8 - 984 - 849

I am told that there are two more such numbers n under 100. How do you find them? And please explan your reasoning. Thanks!

I just found another 27, but I dont know why it is one of the numbers. Please explain! thanks!

such that if n divides a three digit number say ABC where A = hundreds, B = tens, C = ones. Then n also divides BCA and CAB.

So far I have worked out that 1 is special of course, so is 3 (factor test sum of digits will always be the same) and 9 as well as 111,222,333....999 and any number greater than 1000 as it will only divide into the 3 digit number 000.

Also worked out: n cannot be:

n - divides this - not this

2 - 132 - 321

4 - 492 - 249

5 - 335 - 353

6 - 336 - 363

7 - 861 - 618

8 - 984 - 849

I am told that there are two more such numbers n under 100. How do you find them? And please explan your reasoning. Thanks!

I just found another 27, but I dont know why it is one of the numbers. Please explain! thanks!