A number is said to be a crazy number if the sum of its digits is equal to the product of its digits. How many two-digit crazy numbers exist?
Question
A number is said to be a crazy number if the sum of its digits is equal to the product of its digits. How many two-digit crazy numbers exist?
Solution
Sure, let's solve this step by step:
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First, let's understand the problem. A two-digit crazy number is a number where the sum of its digits is equal to the product of its digits. For example, if we have a number 23, the sum of its digits is 2+3=5 and the product of its digits is 2*3=6. So, 23 is not a crazy number because 5 is not equal to 6.
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Now, let's find out all the two-digit crazy numbers. We know that a two-digit number ranges from 10 to 99. So, we need to check all these numbers one by one.
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We start with 10. The sum of its digits is 1+0=1 and the product of its digits is 1*0=0. So, 10 is not a crazy number.
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We continue this process for all the numbers from 10 to 99.
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After checking all the numbers, we find that there are only four two-digit crazy numbers: 12, 21, 13, and 31.
So, there are 4 two-digit crazy numbers.
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