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Problem of the Week 859

Four Non-Fours

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Find an expression for 24 in which 1, 3, 4 and 6 each appear exactly once, while nothing beyond the four operations +, -, x, and /, along with any brackets required, is used.

Source: Lee Sallows, Nijmegen, The Netherlands

For enthusiasts:

  1. Let a, b, c, d be real numbers. What is the largest possible size of S, where a real number is in S if it can be obtained from expressions in which a, b, c, d are each used exactly once and which use nothing beyond the four operations, +, -, x, and / (along with any necessary brackets).

  2. Find integers a, b, c, d so that 0, 1, 2, 3, ..., n are in S and n is as large as possible.

© Copyright 1998 Stan Wagon. Reproduced with permission.

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The Math Forum

2 October 1998