- #1
MGS
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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 don't 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 don't know why it is one of the numbers. Please explain! thanks!