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Posers and Puzzles

Posers and Puzzles

  1. 02 Nov '04 12:01
    It was Joshua's birthday party and being a surprisingly clever lad for his age he decided to challenge his friends to a little game.

    "If anyone can guess the number I'm thinking of they will get a special prize!" he announced.

    "I will give you just four clues," he continued.

    "One. It is made up of five distinct, non-zero digits.

    "Two. The first two digits form the square of the third.

    "Three. The last two digits form a number one less than the square of my age.

    "Four..."

    However before he could give the final clue, Jemma being an equally astute little girl, shouted out the answer with 100% certainty that she was correct and thus claimed the prize.

    What was the number Joshua was thinking of?
  2. Standard member telerion
    True X X Xian
    02 Nov '04 12:56
    Originally posted by tommyg007
    It was Joshua's birthday party and being a surprisingly clever lad for his age he decided to challenge his friends to a little game.

    "If anyone can guess the number I'm thinking of they will get a special prize!" he announced.

    "I will give you just four clues," he continued.

    "One. It is made up of five distinct, non-zero digits.

    "Two. ...[text shortened]... that she was correct and thus claimed the prize.

    What was the number Joshua was thinking of?
    18324.
  3. Standard member Elias5891
    Panda
    02 Nov '04 16:18
    81924.

    By clue 1 & 2, the first digits must be 164, 255, 366, 497, 648, or 819.

    By clue 3, the last two digits must be 15, 24, 35, 48, or 63.

    If you combine all the combinations that do not let a digit repeat:
    16435, 49715, 49735, 49763, 64815, 64835, 81924, 81935, 81963,
    and you know the girl, who knew the boy's age, would know the last two digits, it must be the possibility with the unique last two digits, i.e., 81924
  4. 02 Nov '04 16:56
    Correct!! A gold star to Elias5891
  5. Standard member telerion
    True X X Xian
    02 Nov '04 21:04
    Originally posted by tommyg007
    Correct!! A gold star to Elias5891
    Oops I misread the question. I thought that the first two digits squared formed the last three digits.

    Interestingly enough my answer is the unique solution if read that way.
    18^2 =324

    5^2 - 1= 24