AMC 10 Step by Step
2002 AMC 10AProblem 3P1-10~3 minPrint

According to the standard convention for exponentiation, 2222=2(2(22))=216=65536.2^{2^{2^{2}}} = 2^{(2^{(2^2)})} = 2^{16} = 65536.

If the order in which the exponentiations are performed is changed, how many other values are possible?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site. Also appeared as 2002 12A #3.