- 24 Oct '08 05:40I will pick a number, an integer of say, 6 or more digits. Now I'll make another number by re-arranging those same digits to a different permutation of the original. Then subtract the smaller from the larger number. and from the difference, I'll select one non-zero digit to keep secret. If I reveal the other digits of the difference, in no particular order, how would you determine the secret digit?
- 25 Oct '08 01:16

yes, a good math magic trick*Originally posted by luskin***I will pick a number, an integer of say, 6 or more digits. Now I'll make another number by re-arranging those same digits to a different permutation of the original. Then subtract the smaller from the larger number. and from the difference, I'll select one non-zero digit to keep secret. If I reveal the other digits of the difference, in no particular order, how would you determine the secret digit?** - 26 Oct '08 20:32 / 1 edit

Do you have a proof for it?*Originally posted by doodinthemood***I'm thinking you add up all the digits you tell me, then cast out nines and give the value that makes it add up to 9.**

IE. You say "4,5,2,6,4" and I think "4+5 = 9, + 2 = 2, + 6 = 8, + 4 = 9 + 3 = 3. So the missing digit is 6" - 03 Nov '08 13:10

Let SOD be the function that, with any number as input, gives the Sum Of Digits of that number.*Originally posted by Thomaster***Do you have a proof for it?**

To prove: SOD(A) is dividable by 9 i.a.o.i. A is dividable by 9

Proof:

Let A = a*1 + b*10 + c*100 + d*1000 + ....

A mod 9 = a*1 + b*1 + c*1 + d*1 +... mod 9 = SOD(A) mod 9

Thus, if 9 divides A then 9 also divides SOD(A) and vise versa. - 05 Nov '08 11:07

nice. this same modulo arithmetic argument works for proving most of the classic divisibility rules we all know and love. (taking the digit sum and checking for divisibility by 3 or 9... etc.)*Originally posted by TheMaster37***Let SOD be the function that, with any number as input, gives the Sum Of Digits of that number.**

To prove: SOD(A) is dividable by 9 i.a.o.i. A is dividable by 9

Proof:

Let A = a*1 + b*10 + c*100 + d*1000 + ....

A mod 9 = a*1 + b*1 + c*1 + d*1 +... mod 9 = SOD(A) mod 9

Thus, if 9 divides A then 9 also divides SOD(A) and vise versa.