Difference between revisions of "2021 JMPSC Accuracy Problems/Problem 14"
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+ | ==See also== | ||
+ | #[[2021 JMPSC Sprint Problems|Other 2021 JMPSC Sprint Problems]] | ||
+ | #[[2021 JMPSC Sprint Answer Key|2021 JMPSC Sprint Answer Key]] | ||
+ | #[[JMPSC Problems and Solutions|All JMPSC Problems and Solutions]] | ||
+ | {{JMPSC Notice}} |
Revision as of 16:19, 11 July 2021
Contents
[hide]Problem
What is the leftmost digit of the product
Solution
We notice that In addition, we notice that
Since
We conclude that the leftmost digit must be .
~Bradygho
Solution 2
By multiplying out , , and , we notice that the first digits don't change even when we continue to add more digits. With this observation, we can conclude that the first digit of the product is .
~Mathdreams
Solution 3
Remove factors of and to get . Recall by Pascal's triangle that , , so the leftmost digit is guaranteed to be . Now, multiplying by our scale factor the answer is ~Geometry285
See also
The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition.