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

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==Solution== | ==Solution== | ||

− | + | We notice that | |

+ | <cmath>16000\cdots \times 25000\cdots = 16 \times 25 \times 10^{198} = 400 * 10^{198}</cmath> | ||

+ | In addition, we notice that | ||

+ | <cmath>16200\cdots \times 25300\cdots = 162 \times 253 \times 10^{194} = 40986 \times 10^{194}</cmath> | ||

+ | |||

+ | Since | ||

+ | <cmath>16000\cdots \times 25000\cdots < \underbrace{161616 \cdots 16}_{100 \text{ digits }} \times \underbrace{252525 \cdots 25}_{100 \text{ digits }} < 16200\cdots \times 25300\cdots</cmath> | ||

+ | |||

+ | We conclude that the leftmost digit must be <math>\boxed{4}</math>. |

## Revision as of 22:52, 10 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 .