Problem 1106. I've got the power! (Inspired by Project Euler problem 29)

Created by James

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Consider all integer combinations of a^b and b^a for the integer values 2 ≤ a ≤ 4 and 2 ≤ b ≤ 5:

    2^2=4,  2^3=8,   2^4=16,  2^5=32
    3^2=9,  3^3=27,  3^4=81,  3^5=243
    4^2=16, 4^3=64,  4^4=256, 4^5=1024
    5^2=25, 5^3=125, 5^4=625

If they are then placed in numerical order, with any repeats removed, we get the following sequence of 14 distinct terms:

4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024

Given two values for x and y, find the unique, sorted sequence given by the values a^b and b^a for 2≤a≤x and 2≤b≤y.

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Last Solution submitted on Apr 16, 2025

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@bmtran (Bryant Tran) on 7 Dec 2012

What your problem description asks for and what your test suite asks for are different. Specifically, test case 4 requires that the operation be commutative, which, by your problem statement, it is not (since the power function itself is not commutative). This is reflected in the other test cases as well. (also, you call your arguments x and y in the description and a and b in the template).

James on 7 Dec 2012

You are correct. I had the "and b^a" in there originally, but I accidentally deleted it when I added the "for 2≤a≤x and 2≤b≤y" text. It's fixed now, and the description should be a bit clearer.

@bmtran (Bryant Tran) on 7 Dec 2012

thanks James!

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Problem 1106. I've got the power! (Inspired by Project Euler problem 29)

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Last 200 Solutions

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Problem 1106. I've got the power! (Inspired by Project Euler problem 29)

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Last 200 Solutions

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Problem Recent Solvers131

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