Michael Reid’s Happy New Year Puzzle

Here is another puzzle from Michael Reid on NOBNET. (Michael also notes that if you find a solution (a,b,c,d,e,f) then (d,e,f,a,b,c) is another solution.)

Puzzle: Replace a, b, c, d, e, f with the first six prime numbers, in some order, to make the expression a * b^c + d * e^f equal to the New Year.

Best wishes for a happy, healthy and prosperous New Year!

One thought on “Michael Reid’s Happy New Year Puzzle

  1. Thanks for posting!

    ***SPOILERS***

    Found the two solutions by brute force in Sage:

    primes = primes_first_n(6)
    func(a, b, c, d, e, f) = a * b^c + d * e^f
    for a in permutations(primes):
    ….: if func(*a) == 2012:
    ….: print a
    ….:
    [11, 5, 3, 13, 7, 2]
    [13, 7, 2, 11, 5, 3]

    Or a two-liner:

    func(a, b, c, d, e, f) = a * b^c + d * e^f
    [a for a in permutations(primes_first_n(6)) if func(*a) == 2012]

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