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Fair and Square (Posted on 2003-11-03) Difficulty: 3 of 5
Jack and Jill each have marble collections. The number in Jack's collection in a square number.

Jack says to Jill, "If you give me all your marbles I'll still have a square number." Jill replies, "Or, if you gave me the number in my collection you would still be left left with an even square."

What is the fewest number of marbles Jack could have?

  Submitted by Ravi Raja    
Rating: 2.3333 (3 votes)
Solution: (Hide)
25

Jack has 25 marbles and Jill has 24. If Jill gives Jack all her marbles, he will have 49(7²), and if Jack gives Jill the number in her collection, he will be left with one, which is a square.

This ignores the trivial case where Jill has 0 marbles, since they problem says they each have marble collections, they must each have some marbles in their collections.

DJ provided a good proof of why this is the minimum here.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some ThoughtsPuzzle AnswerK Sengupta2024-02-09 21:06:28
SolutionPossible Solutionbroll2022-05-20 00:17:08
AnswerK Sengupta2008-03-20 09:35:31
Ravi TriplesLee2003-11-04 00:53:02
re: Fuller SolutionCharlie2003-11-03 22:09:37
part 2 of the mayhem of my previous postVictor Zapana2003-11-03 19:20:53
solutions for some possibilities part 1Victor Zapana2003-11-03 19:07:09
SolutionFuller SolutionDJ2003-11-03 18:52:02
re(7): Lost their marbles (full solution)SilverKnight2003-11-03 17:16:21
re(6): Lost their marbles (full solution)DJ2003-11-03 17:07:08
re: Dead HorseSilverKnight2003-11-03 15:24:42
Dead Horsenikki2003-11-03 15:09:02
re(5): Lost their marbles (full solution)SilverKnight2003-11-03 13:48:01
re(4): Lost their marbles (full solution)DJ2003-11-03 13:45:04
re(3): Lost their marbles (full solution)SilverKnight2003-11-03 13:39:24
re(2): Lost their marbles (full solution)DJ2003-11-03 13:36:30
re: Lost their marbles (full solution)SilverKnight2003-11-03 12:54:39
SolutionLost their marbles (full solution)DJ2003-11-03 12:37:34
re(3): solutionSilverKnight2003-11-03 11:12:07
re(2): solutionSilverKnight2003-11-03 10:59:55
re: solutionCharlie2003-11-03 10:54:27
This is terrible.....Dan2003-11-03 10:32:22
SolutionsolutionSilverKnight2003-11-03 10:06:42
re: not sure if this countsKitty Saturn2003-11-03 09:06:15
Hints/Tipsnot sure if this countsFatBoy2003-11-03 08:25:16
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