2021 JMPSC Accuracy Problems/Problem 14
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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
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