Solving A Mathematical Puzzle

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Do you feel lost when presented with a word problem, a puzzle, or a real-life scenario where you know they need to use mathematics to get an answer? Do you just not know where to begin?

Many people have expressed to me that this is how they feel. So in this post, I’m going to give you a real-life puzzle from a mathematical calendar and show you every part of both finding the answer and proving it — being certain your answer is right, and will always be right, 100% of the time.

In formal mathematical proofs, brevity is the highest goal. The shorter a proof is, so long as it’s complete, the better. A shorter proof is more elegant and represents much greater clarity of thought.

In this post, I’m not going to go for the shortest path to an answer because my goal is primarily to give readers a sense of the process of solving a puzzle. How to analyze it, think about it, and go about finding an answer. Then how to prove the answer is correct.

Here is the problem:

If we can solve this, it will be quite a fun victory. And because the sum of the digits of a number often has a relationship to its factors, it will be a nice “bring it all together moment” for aspects of algebra we’ve talked about before.

What is the sum of the digits of a number? Exactly what it sounds like. The sum of the digits of the current year is: 2 + 0 + 2 + 5 = 9.

The wording of this problem implies that if we take any three-digit number and multiply it by 999, the sum of the digits will always be the same.

So let’s start with seeing if that seems to be true. If it does, then we’ll see if we can prove that it’s always true.

Holly’s Substack

Solving A Mathematical Puzzle

How to Not Suck at Math, part 15

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