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We call a number cozy if every digit in the number is either even or next to an even digit.  For example, a number is cozy if every digit in the number is either a 2 or next to a 2.  For example, the number 222, 72, 45, and 810 and are all cozy.  Also, the numbers 202 and 2772 are cozy.

 

How many 2-digit numbers are cozy?

 Jun 3, 2024
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There are actually more 2-digit numbers that are cozy than not. 

 

We can just list them out!

\(11,13,15,17,19 \\ 31,33,35,27,39 \\ 51,53,55,57,59 \\ 71,73,75,77,79 \\ 91,93,95,97,99\)

 

These numbers are those who are not cozy. Counting through them, there are 25. 

 

In total, there are 90 two-digit numbers, so we have

 

90 - 25 = 65. 

 

So 65 two-digit numbers are cozy. 

 

Thanks! :)

 Jun 3, 2024

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