Date: Sat, 26 Oct 96 18:01:00

From: Alex Bogomolny

Dear Tobias,

Thanks for your problem. You are right. 8 seems the hardest part of it indeed. I doubt there exists another number besides 6 with all ten representations by three digits. 3 would seem rather a natural candidate but I got stuck on digit 6 and for 5, the only solution I could think of used periodic decimals. Can you do any better?

On the other hand, if you decide to use 4 digits instead of 3, then number 4 can be represented by 4 digits and arithmetic operations (including the square root and factorials). Are there other numbers with this property?

Sincerely,

Alex

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