# secret digit

luskin
Posers and Puzzles 24 Oct '08 05:40
1. 24 Oct '08 05:40
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?
2. 24 Oct '08 06:30
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"
3. 24 Oct '08 09:50
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"
Yep that's it.
4. Palynka
Upward Spiral
24 Oct '08 14:273 edits
Originally posted by luskin
Yep that's it.
Edit - I really need to learn how to read. ðŸ˜ž
5. joe shmo
Strange Egg
25 Oct '08 01:16
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?
yes, a good math magic trick
6. AThousandYoung
26 Oct '08 14:36
This thread looks perverted. Secret digit, my arse.

Wait no, don't put it there, on second thought.
7. 26 Oct '08 20:321 edit
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"
Do you have a proof for it?
8. TheMaster37
Kupikupopo!
03 Nov '08 13:10
Originally posted by Thomaster
Do you have a proof for it?
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.
9. 05 Nov '08 11:07
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.
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.)