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Below are the answers to our 2013 Maths Masters' Summer Quiz. The detailed solutions can be downloaded here: Easy, Medium and Hard.

If you're looking for more puzzles, you can check out our previous quizzes: the 2012 Quiz; the 2011 Quiz; the 2010 Quiz; the 2009 Quiz; the 2008 Quiz.


Easy 1: 45 and 40.
Easy 2: The circumference.
Easy 3: The only pair is 2 and 997.
Easy 4: 7 pages.
Easy 5: 1.
Easy 6: 1/16 and 1/4.
Easy 7: 5.
Easy 8: 13.
Easy 9: 372 votes.
Easy 10: The number in the top left corner is 16.


Medium 1: 73.
Medium 2: 1/3.
Medium 3: 13 marbles.
Medium 4: Niels.
Medium 5: More than half.
Medium 6: A loss of 69 cents.
Medium 7: 2 helpers.
Medium 8: 2/3.
Medium 9: 17 and 45.
Medium 10: Take 1, 2 and 3 bars from the piles.


Hard 1: (3, 8, 35), (4, 7, 30) and (5, 6, 28).
Hard 2: 25/74.
Hard 3: The areas are equal.
Hard 4: 3 moves.
Hard 5: 14.5 meters.
Hard 6: The other possibilities are the sequences starting with 14 and 25.
Hard 7: 120 ounces.
Hard 8: 5050.
Hard 9: The left side.
Hard 10: If you have 11 different nets then you’re done!

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