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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?

 

How many 3-digit numbers are cozy?

 Mar 3, 2023

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A) we have that all numbers between 20-30, 40-50, 60-70 etc are cozy. This equates to 10*4 = 40 cozy numbers already. We now have that every other number (in odd 10th place numbers) is cozy. lets use 30-40 as an example. 31 is not cozy, but 32 is. we also have that 34, 36 and 38 are cozy. Applying this to 1-20, 30-40, 50-60, 70-80, 90-100, we get that 4*5 = 20. This means there are 60 cozy 2 digit numbers. (I used a inefficient method, correct me if i got something wrong!)
Hope this Helps!
 Mar 3, 2023

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