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What Number am I? – Combination of digits

Math Teaser

I am 3 digits. My digits add up to 10. The product of my digits is 20. I am an odd number. The digit in the hundreds place plus the digit in the tens place equals the digit in the ones place. The smallest digit is in the middle.

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The most basic approach to this problem is to select some digits and see if they meet the criteria. In this case, with some trial and error, it isn’t too difficult to find that the values 4,5, and 1 can add to 10 and multiply to 20. Use the clues to determine the order, and you have 415 as the answer.

A mathematical solution was also built in to the problem. You can write the equation for the sum of the digits as a + b + c = 10. Knowing that the first 2 digits add together to equal the last digit, written as a + b = c, you can rewrite the sum equation as (a + b) + c = 10 or c + c =10 or 2c = 10. Use basic algebra and divide both sides by 2 and c = 5. You have solved for the value of the third digit. It is now simpler to select values that satisfy the addition and multiplication conditions. What two numbers add up to 5 and also can be multiplied together and then by 5 to equal 20? The answers are much easier to see with such a limited set of possibilities. Only a 1 and a 4 can meet the conditions with the 5 as the third digit. The last clue tells you the order. 415 is the answer.