Difference between revisions of "2024 AIME II Problems/Problem 14"

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==Problem==
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Let b2 be an integer. Call a positive integer n b-eautiful if it has exactly two digits when expressed in base b  and these two digits sum to n. For example, 81 is 13-eautiful because 81=6 313 and 6+3=81. Find the least integer b2 for which there are more than ten b-eautiful integers.
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==See also==
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{{AIME box|year=2024|num-b=13|num-a=15|n=II}}
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[[Category:Intermediate Algebra Problems]]
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{{MAA Notice}}

Revision as of 09:30, 9 February 2024

Problem

Let b2 be an integer. Call a positive integer n b-eautiful if it has exactly two digits when expressed in base b and these two digits sum to n. For example, 81 is 13-eautiful because 81=6 313 and 6+3=81. Find the least integer b2 for which there are more than ten b-eautiful integers.

See also

2024 AIME II (ProblemsAnswer KeyResources)
Preceded by
Problem 13
Followed by
Problem 15
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions

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