Brain Teaser Week: Answers Edition!

Did you enjoy Brain Teaser Week, fellow puzzlers and PuzzleNationers? We certainly hope so! It was a fun experiment in dedicating an entire week to a particular type of puzzle.

We gave you three puzzles to challenge your deductive, mathematical, and puzzly skills, and now it’s time to break them down and explain them.


Tuesday’s Puzzle:

A set of football games is to be organized in a “round-robin” fashion, i.e., every participating team plays a match against every other team once and only once.

If 105 matches in total are played, how many teams participated?

If every team plays every other team once, you can easily begin charting the matches and keeping count. With 2 teams (Team A and Team B), there’s 1 match: AB. With 3 teams (A, B, and C), there are 3 matches: AB, AC, BC. With 4 teams (A, B, C, and D), there are 6 matches: AB, AC, AD, BC, BD, CD. With 5 teams (A, B, C, D, and E), there are 10 matches: AB, AC, AD, AE, BC, BD, BE, CD, CE, DE.

Now, we could continue onward, writing out all the matches until we reach 105, but if you notice, a pattern is forming. With every team added, the number of potential matches increases by one.

With one team, 0 matches. With two teams, 1 match. With three teams, 2 more matches (making 3). With four teams, 3 more matches (making 6). With five teams, 4 more matches (making 10).

So, following that pattern, 6 teams gives us 15, 7 teams gives us 21, and so on. A little simple addition tells us that 15 teams equals 105 matches.


Thursday’s Puzzle:

You want to send a valuable object to a friend securely. You have a box which can be fitted with multiple locks, and you have several locks and their corresponding keys. However, your friend does not have any keys to your locks, and if you send a key in an unlocked box, the key could be copied en route.

How can you and your friend send the object securely?

(Here’s the simplest answer we could come up with. You may very well have come up with alternatives.)

The trick is to remember that you’re not the only one who can put locks on this box.

Put the valuable object into the box, secure it with one of your locks, and send the box to your friend.

Next, have your friend attach one of his own locks and return it. When you receive it again, remove your lock and send it back. Now your friend can unlock his own lock and retrieve the object.

Voila!


Friday’s Puzzle:

The owner of a winery recently passed away. In his will, he left 21 barrels to his three sons. Seven of them are filled with wine, seven are half full, and seven are empty.

However, the wine and barrels must be split so that each son has the same number of full barrels, the same number of half-full barrels, and the same number of empty barrels.

Note that there are no measuring devices handy. How can the barrels and wine be evenly divided?

For starters, you know your end goal here: You need each set of barrels to be evenly divisible by 3 for everything to work out. And you have 21 barrels, which is divisible by 3. So you just need to move the wine around so make a pattern where each grouping (full, half-full, and empty) is also divisible by 3.

Here’s what you start with:

  • 7 full barrels
  • 7 half-full barrels
  • 7 empty barrels

Pour one of the half-full barrels into another half-full barrel. That gives you:

  • 8 full barrels
  • 5 half-full barrels
  • 8 empty barrels

If you notice, the full and empty barrels increase by one as the half-full barrels decrease by two. (Naturally, the total number of barrels doesn’t change.)

So let’s do it again. Pour one of the half-full barrels into another half-full barrel. That gives you:

  • 9 full barrels
  • 3 half-full barrels
  • 9 empty barrels

And each of those numbers is divisible by 3! Now, each son gets three full barrels, one half-full barrel, and three empty barrels.


How did you do, fellow puzzlers? Did you enjoy Brain Teaser Week? If you did, let us know and we’ll try again with another puzzle genre!

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The Conclusion of Brain Teaser Week!

It’s the third and final day of our celebration of all things brain-teasing, riddling, and word-tricky, and we’ve got one last devious challenge lined up for you.

Remember! On Tuesday, Thursday, and Friday of this week, a different brain teaser or word problem will be posted, and it’s up to you to unravel them. Contact us with the correct answer — either here on the blog through the comments, or on Twitter, Facebook, or Instagram through our messages — and you’ll be entered into a pool to win a prize!

And yes, you can enter more than once! Heck, if you solve Tuesday, Thursday, AND Friday’s puzzles, that’s three chances to win!

Let’s get started, shall we?


Here’s today’s brain teaser, which mixes the math of Tuesday’s puzzle with the deductive reasoning of Thursday’s puzzle:

The owner of a winery recently passed away. In his will, he left 21 barrels to his three sons. Seven of them are filled with wine, seven are half full, and seven are empty.

However, the wine and barrels must be split so that each son has the same number of full barrels, the same number of half-full barrels, and the same number of empty barrels.

Note that there are no measuring devices handy. How can the barrels and wine be evenly divided?


Good luck, fellow puzzlers! We’ll see you Tuesday with answers for all three brain teasers!

Thanks for visiting PuzzleNation Blog today! Be sure to sign up for our newsletter to stay up-to-date on everything PuzzleNation!

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Brain Teaser Week Continues!

It’s Day 2 of our celebration of all things mind-tickling, and we’ve got another diabolical challenge lined up for you.

Remember! On Tuesday, Thursday, and Friday of this week, a different brain teaser or word problem will be posted, and it’s up to you to unravel them. Contact us with the correct answer — either here on the blog through the comments, or on Twitter, Facebook, or Instagram through our messages — and you’ll be entered into a pool to win a prize!

And yes, you can enter more than once! Heck, if you solve Tuesday, Thursday, AND Friday’s puzzles, that’s three chances to win!

Let’s get started, shall we?


Here’s today’s brain teaser, which is less mathematical than Tuesday’s and more logical or deductive:

You want to send a valuable object to a friend securely. You have a box which can be fitted with multiple locks, and you have several locks and their corresponding keys. However, your friend does not have any keys to your locks, and if you send a key in an unlocked box, the key could be copied en route.

How can you and your friend send the object securely?


Good luck, fellow puzzlers! We’ll see you Friday with our next brain teaser!

Thanks for visiting PuzzleNation Blog today! Be sure to sign up for our newsletter to stay up-to-date on everything PuzzleNation!

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Welcome to Brain Teaser Week!

[Image courtesy of Bogoreducare.org.]

Hello puzzlers and PuzzleNationers!

This week I thought I would try something different and focus on a theme for the week’s posts, rather than posting about different topics on our usual days.

So, please join me in some puzzly challenges as we celebrate Brain Teasers Week here at PuzzleNation Blog.

On Tuesday, Thursday, and Friday of this week, a different brain teaser or word problem will be posted, and it’s up to you to unravel them. Contact us with the correct answer — either here on the blog through the comments, or on Twitter, Facebook, or Instagram through our messages, and you’ll be entered into a pool to win a prize!

And yes, you can enter more than once! Heck, if you solve Tuesday, Thursday, AND Friday’s puzzles, that’s three chances to win!

Let’s get started, shall we?


Here’s today’s brain teaser:

A set of football games is to be organized in a “round-robin” fashion, i.e., every participating team plays a match against every other team once and only once.

If 105 matches in total are played, how many teams participated?


Good luck, fellow puzzlers! We’ll see you Thursday with our next brain teaser!

Thanks for visiting PuzzleNation Blog today! Be sure to sign up for our newsletter to stay up-to-date on everything PuzzleNation!

You can also share your pictures with us on Instagram, friend us on Facebook, check us out on TwitterPinterest, and Tumblr, and explore the always-expanding library of PuzzleNation apps and games on our website!

Brain Teaser: A Curious Way to Tell Time

We love tackling brain teasers, riddles, math puzzles, and mind ticklers here at PuzzleNation Blog.

Our friends at Penny Dell Puzzles also enjoy putting their puzzly skills to work by posting various brain teasers..

And one of our mutual readers was hoping we could explain how to solve a puzzle that recently made the rounds on Penny’s social media accounts.

We’d be happy to!

Today, let’s take a look at a brain teaser all about time.

So, where do we begin?

Let’s start by breaking that sentence down to make it easier to parse: “The number of hours left today is half of the number of hours already passed.”

Well, a simpler way of saying that is “the number of hours already passed is twice the number of hours left.”

So if you have the number of hours left — let’s call that X — then the number of hours already passed is twice X, or 2X. Between X and 2X, that’s your entire day covered.

Sorting that out gives us the simple formula of X + 2X = 24, since there are 24 hours in a day.

That easily becomes 3X = 24, and simple division tells us that X = 8.

So X, the number of hours left today, is 8. Which means that twice X, or 16, is the number of hours already passed.

And if there are 8 hours left in the day (or 16 hours already passed), that means it’s 4 PM.


Most of the time, brain teasers are all about efficiently organizing the information we have.

That allows us to figure out how best to use that information to move forward and solve the puzzle. This is just as true with a relatively straightforward brain teaser like this as it is with a complicated logic puzzle with all sorts of pieces to put together.

It’s all about figuring out what we know, what we don’t, and how what we DO know can lead us to what we don’t.

That’s just part of the fun.


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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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You can also share your pictures with us on Instagram, friend us on Facebook, check us out on TwitterPinterest, and Tumblr, and explore the always-expanding library of PuzzleNation apps and games on our website!