Difference between revisions of "1988 AIME Problems"
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== Problem 9 == | == Problem 9 == | ||
+ | Find the smallest positive integer whose [[perfect cube|cube]] ends in <tt>888</tt>. | ||
[[1988 AIME Problems/Problem 9|Solution]] | [[1988 AIME Problems/Problem 9|Solution]] |
Revision as of 12:47, 24 October 2007
Contents
[hide]Problem 1
One commercially available ten-button lock may be opened by depressing -- in any order -- the correct five buttons. The sample shown below has as its combination. Suppose that these locks are redesigned so that sets of as many as nine buttons or as few as one button could serve as combinations. How many additional combinations would this allow?
Problem 2
For any positive integer , let denote the square of the sum of the digits of . For , let . Find .
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Find the smallest positive integer whose cube ends in 888.