A number theory problem by A Former Brilliant Member

Number Theory Level 2

How many 7-digit numbers that do not start nor end with 1 are there?


The answer is 7200000.

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

Chris Lewis
Dec 10, 2019

There are 8 8 choices for the first digit, 9 9 choices for the last digit, and 10 10 choices for each of the other digits, giving a total of 8 × 9 × 1 0 5 = 7200000 8 \times 9 \times 10^5=\boxed{7200000} such numbers.

4 Helpful 1 Interesting 2 Brilliant 0 Confused
Max Patrick
Dec 11, 2019

Every number from 2000000 to 9999999 (8 million numbers) except a tenth of these which end in 1. 8000000x9/10 = 7200000

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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