Solving A Mathematical Puzzle

How to Not Suck at Math, part 15

This is my series on how to get better at math.

Previous posts in the series:

Part 1: Addition and Subtraction

Part 2: Multiplication, Division, and Fractions

Part 3: The Major Key of Mathematical Fluency

Part 4: A Proof for this Approach to Numeracy

Part 5: “I’m Just Not A Math Person!”

Part 6: How the Sign Rules Work, and Why

Part 7: The Box Method of Multiplication

Part 8: Elite Mathematical Training

Part 9: An Extremely Cool Math Trick

Part 10: The One Where Algebra Starts Making Sense

Part 11: The One Thing Everyone Remembers From High School

Part 12: How to Solve Those Viral Math Memes

Part 13: How to Impress Your Kids

Part 14: How to Show Off Mental Math

Posts 1-5 are not behind the paywall. Parts 6 and beyond are, but this link will give you 10% off. If you’d like to get them but can’t afford a paid subscription, email me at hollymathnerd at gmail dot com and I’ll give you a free one.

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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.

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