# A Dollar For Your Thoughts? It’s the Hundred Dollar Puzzle!

[Image courtesy of ColourBox.com.]

That’s right, fellow puzzlers and PuzzleNationers! It’s that time again when we pit our puzzly minds against a fiendish brain teaser and test our mental mettle!

You might’ve seen this brain teaser making the rounds on social media. It’s known as the hundred dollar puzzle, and unlike most brain teasers, this one is less about the puzzle and more about how we got to the solution.

Intrigued? You’re not the only one. Let’s take a look at the brain teaser:

A young man sees a shirt for \$97. He borrows \$50 from mom and \$50 from dad. He buys the shirt and is left with \$3 change.

He gives \$1 to mom, \$1 to dad, and keeps \$1 for himself. Now he owes his mom \$49 and his dad \$49.

\$49 + \$49 = \$98 + his remaining \$1 = \$99. Where did the other \$1 go?

[Image courtesy of CollecTons.]

People love brain teasers like this, because at first glance, and even at second glance, the math SEEMS to hold up.

But the real trick to this one is that it’s asking the wrong question. The other dollar didn’t go anywhere.

The problem here is… as soon as he pays his parents back, it’s no longer about one hundred dollars. It’s about ninety-eight dollars.

Let’s look at total borrowings versus borrowings after paying back his parents. The original specs were:

What he owed: \$100
What he had: \$3 and a \$97 dollar shirt.

But the goalposts changed when he paid his parents back a dollar each. (And if he plans to pay the loan off a dollar at a time, it’s going to take FOREVER for them to get their money back.)

What he now owes: \$98
What he has: \$1 and a \$97 dollar shirt.

The math adds up. Your total borrowings go from \$100 to \$98 dollars, and you spent \$97 dollars and put the extra dollar in your pocket.

So the final equation in the brain teaser is flawed. It’s not \$49 + \$49 = \$98 + his remaining \$1 = \$99. It’s \$49 + \$49 = \$98 = his remaining \$1 and his fancy shirt \$97.

[Image courtesy of Ali Express.com.]

Sometimes, brain teasers aren’t about crunching numbers, but finding the logical flaw in the puzzle itself.

We hope you enjoyed unraveling the hundred dollar puzzle, and if you have any brain teasers, riddles, or other puzzly suggestions for mental challenges to conquer, let us know in the comment section below! We’d love to hear from you!

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# Let’s Make a Deal!

It’s a scenario every game show fan knows well. You’ve got three doors to choose from, and one of those doors will open to reveal a fabulous prize.

After you’ve made your choice (let’s say Door #2), our affable host Monty Hall plays Devil’s Advocate by opening one of the doors you didn’t choose (let’s say Door #1), revealing a goat or other lackluster result.

And then, Monty offers you a chance to change your mind. Will you stick with the door you initially chose, or will you switch to the other unopened door (Door #3)?

The average player sees two choices, Door #2 and Door #3, which on the surface sounds like a 50/50 shot, a coin flip. So would it surprise you to learn that people who switched from one door to the other doubled their chances to win the fabulous prize?

This is known as the Monty Hall Problem, an example of how statistics aren’t always what they seem, and it has puzzled people for decades.

It’s counterintuitive, isn’t it? I mean, you have two choices, so the odds should be 50/50. But you’re forgetting that third door that Monty eliminated. That third door makes all the difference, statistically speaking.

Let’s break it down. Your initial choice is between 3 doors, meaning you have a 1 in 3 chance of picking the correct door, and a 2 in 3 chance of picking the wrong one.

When Monty opens that other door, the odds haven’t changed. Only the number of options available has changed. Your door is still a 1 in 3 chance of being correct and a 2 in 3 chance of being wrong. But the remaining door now has a 2 in 3 chance of being correct!

So what appeared to be a coin flip between sticking with your choice and switching is now heavily weighted toward switching!

There have been several real-world tests of the Monty Hall Problem, and all of them have consistently shown that the people who switch were twice as likely to open the winning door!

The real puzzle here is how we fool ourselves. We take the numbers at face value — 3 doors become 2 doors, so a 1 in 3 chance becomes a 1 in 2 chance — and actually hurt our chances with those seemingly simple assumptions.

Being able to reconsider your assumptions is a major tool in the puzzler’s solving kit. Plenty of tricky crossword clues depend on you associating the clue with one thing, when the answer is something quite different.

After all, if you saw the clue “Unlocked” for a four-letter entry, you’d probably try OPEN before you tried BALD. Clever constructors are counting on that.

So be sure to remember Monty Hall and his three-door conundrum the next time you’re stumped on a puzzle. Maybe the answer is as simple as trying another door.

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