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avatar+952 

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?

 Mar 15, 2024
 #1
avatar+34 
0

Any two-digit number with a 2 is cozy (and all cozy numbers have at least one 2) There are nine two-digit numbers with ones digit 2 and there are nine additional two-digit numbers with tens digit 2 (excluding 22 which we've already counted, since its ones digits is 2) Therefore, there are 9 + 9 = 18 cozy two-digit numbers.

 Mar 15, 2024
 #2
avatar+128794 
+2

The ones that aren't cozy

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  =    25 numbers

 

Number of two-dgit numbers  =  99 - 10 + 1 =  90

 

So

 

90  - 25  =  65  are cozy

 

cool cool cool

 Mar 16, 2024

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