Math CentralQuandaries & Queries


Question from Janet, a parent:

How many two digit numbers contain at least one number seven?

Hi Janet,

There are 90 two digit numbers 10, 11, 12, ... 99.

1) How many of them have the digit 7 in the units position?

These are 17, 27, ... 97

2) How many of them have the digit 7 in the tens position?

These are 70, 71, 72, ... , 79

Add the answers you got to questions 1 and 2. This isn't the correct answer because you have included the number 77 in 1 and 2 and you should only count it once. Thus the correct answer is

(the answer to 1) plus (the answer to 2) minus 1

I hope this helps,

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