# 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.

• 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!

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!

# 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!

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 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!

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!

# 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!

# Six Years of PuzzleNation Blog (Plus a Contest)!

[Image courtesy of Bogoreducare.org.]

Yes, we’re celebrating today, fellow puzzlers and PuzzleNationers!

We’re celebrating because it is the sixth anniversary of the very first post here on PuzzleNation Blog! Yes, we’ve been on this puzzly journey together since August of 2012, and in my admittedly biased yet humble opinion, it’s been a brilliant one.

In those six years, we’ve published over a thousand posts! (More than nine hundred of them penned by yours truly.) We’ve delved into puzzle history, cracked diabolical brain teasers, marked milestones like the centenary of the crossword, and even rejoiced at puzzly proposals of marriage!

And to celebrate six years of PuzzleNation Blog, we’ve got a week of activities planned for our marvelous readers and fellow puzzlers!

For starters, we’re loading over a hundred new pins to our Pinterest account for your viewing pleasure!

And we’re launching a promotion across all of our social media platforms to celebrate the anniversary. It’s our PuzzleNation 6th Anniversary Contest!

Starting today, and every day for the next five days, we’ll be posting a different brain teaser on Instagram.

Also starting today, keep your eyes peeled on Facebook and Twitter, because each day for the next five days, we’ll be asking for a single answer from that day’s Daily POP Crosswords App puzzle and that day’s Penny Dell Crosswords App puzzle.

(These will be separate from the usual Crossword Clue Challenge posts, and we’ll mark them with “PuzzleNation 6th Anniversary Contest” to distinguish them.)

Message us on FB or Twitter with the answer, or message us on Instagram with the answer to a brain teaser, and you’ll go into a drawing for a terrific prize! (And yes, since there are different brain teasers each day and different answers for each of the two daily puzzles, you can enter multiple times to increase your odds of winning!)

Enjoy the contest, fellow puzzlers. It’s a small thank you for being a part of the PuzzleNation community.

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!

# A Puzzly Story for the Whole Family!

Happy Thanksgiving, fellow puzzlers and PuzzleNationers!

In honor of a day dedicated to family and giving thanks for the many blessings in our lives, I’ve got a puzzly story to share with you.

Let’s start with a brain teaser: Samuel was born first, but his twin brother Ronan is older. How is that possible?

[Image courtesy of Cape Cod Healthcare’s Facebook page.]

The answer? When Daylight Savings Time gets involved.

In the early hours of Sunday, November 6, Emily Peterson was at the hospital with her husband Seth, delivering twin boys. But after the birth of her son Samuel, the time change got involved and made the blessed event a tiny bit stranger.

From an article on Fox News, passed along to me by friend of the blog Gina Kanter:

Emily Peterson gave birth to the first baby, Samuel, at 1:39 a.m., before clocks turned back at 2 a.m. […] Then, 31 minutes later, she delivered Ronan. Because Ronan’s birth came after the time change, his official birth time was 1:10 a.m., not 2:10 a.m.

And although one of the nurses said she’s never seen something like this in 40 years of work as a nurse, the father wasn’t surprised. “I said earlier that night that they were either going to be born on two different days or the time change was going to come into play.”

Of course, we know which child is actually older, but when you look at the delivery times and then ask who is older, it makes for a great story. It’s not every child that inspires a brain teaser on his day of birth, so kudos to Ronan and Samuel for creating a wonderful little puzzly gem.

Have a marvelous holiday!

And don’t forget, our Penny Dell Sudoku app contest ends at midnight tonight! Click here for the full details!

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!