2021 JMPSC Accuracy Problems/Problem 14
What is the leftmost digit of the product
We notice that In addition, we notice that
We conclude that the leftmost digit must be .
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 .
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