How Many Times Will Tom Have To Paint The Number 8? - Math Challenge

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Answer: Tom will have to paint the number 8 a total of 20 times.

Explanation: 

Let S be the set of numbers from 1 to 100. To solve this riddle, we need to determine the cardinality of the subset T of S that consists of all the numbers in S that contain the digit 8.

Firstly, the number 8 is an element of T.

Secondly, for each integer n in the set {18, 28, 38, 48, 58, 68, 78, 88, 98}, the digit 8 appears in the tens digit of n. Thus, each of these integers is an element of T.

Thirdly, for each integer n in the set {80, 81, 82, 83, 84, 85, 86, 87, 88, 89}, the digit 8 appears in the units digit of n. Thus, each of these integers is an element of T.

Therefore, T is the union of the three sets {8}, {18, 28, 38, 48, 58, 68, 78, 88, 98}, and {80, 81, 82, 83, 84, 85, 86, 87, 88, 89}. The cardinality of T is the sum of the cardinalities of these three sets, which is 1 + 9 + 10 = 20.

Hope you enjoyed solving today's math challenge! Don't forget to share it with your friends and challenge them to beat you. And if you're hungry for more math challenges, try these: If 4 men can build 4 tables in 4 hours, how many tables can 8 men build in 8 hours? keep your problem-solving skills sharp and have fun!