# Difference between revisions of "2021 JMPSC Accuracy Problems/Problem 14"

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By multiplying out <math>16 \cdot 25</math>, <math>161 \cdot 252</math>, and <math>1616 \cdot 2525</math>, we notice that the first <math>2</math> 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 <math>4</math>. | By multiplying out <math>16 \cdot 25</math>, <math>161 \cdot 252</math>, and <math>1616 \cdot 2525</math>, we notice that the first <math>2</math> 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 <math>4</math>. | ||

− | ~ Mathdreams | + | ~Mathdreams |

## Revision as of 11:38, 11 July 2021

## 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