Posers and Puzzles

Posers and Puzzles

  1. Joined
    14 Dec '05
    Moves
    5692
    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. Joined
    31 May '07
    Moves
    696
    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. Joined
    14 Dec '05
    Moves
    5692
    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. Standard memberPalynka
    Upward Spiral
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    02 Aug '04
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    8702
    24 Oct '08 14:273 edits
    Originally posted by luskin
    Yep that's it.
    Edit - I really need to learn how to read. 😞
  5. Subscriberjoe shmo
    Strange Egg
    podunk, PA
    Joined
    10 Dec '06
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    7733
    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. SubscriberAThousandYoung
    iViva la Hispanidad!
    tinyurl.com/y2c6j2t3
    Joined
    23 Aug '04
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    24791
    26 Oct '08 14:36
    This thread looks perverted. Secret digit, my arse.

    Wait no, don't put it there, on second thought.
  7. ALG
    Joined
    16 Dec '07
    Moves
    6190
    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. Standard memberTheMaster37
    Kupikupopo!
    Out of my mind
    Joined
    25 Oct '02
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    20443
    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. Joined
    02 Mar '06
    Moves
    17881
    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.)
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