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Weekly Problem 41 - 2006

Stage: 3 Challenge Level: Challenge Level:1
One cake and one bun cost a total of 62p. Note that 512 = 8 x 62 + 16, and note also that 16 = 39 - 23. Hence

512 = 8(39 + 23) + 16 = 8(39 + 23) + 39 - 23 = 9 x 39 + 7 x 23.

As 39 and 23 do not have a common factor other than 1, Helen must have bought 9 cakes and 7 buns.

This problem is taken from the UKMT Mathematical Challenges.

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