# 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!

# Meet the Daily POP Crosswords Constructors: Bonnie L. Gentry

One of the Daily POP Crosswords app’s best features is the level of involvement from topnotch constructors. We’ve assembled one heck of a team when it comes to creating terrific, exciting, fresh themed crosswords.

And over the next few weeks, we’ll be introducing you to some of them. Some names you may know, some you may not, but they’re all doing amazing work on these puzzles and deserve a little time in the limelight.

In this installment, allow us to introduce you to constructor Bonnie L. Gentry!

How did you get started in crosswords?

I sold my first puzzle in 2003 to The Los Angeles Times after I discovered a community of crossword constructors on the website Cruciverb.com. It had style sheets and contact information so I gave it a shot.

I have since been published in The New York Times, Wall Street Journal, USA Today, Crosswords Club, and several crossword books. I also construct a two-page newspaper crossword each Thanksgiving for numerous newspapers.

I’m only a casual solver. I enjoy constructing much more. I tried only twice to compete in a national crossword tournament (ACPT), but ranked miserably. Switching to judging was far easier.

What do you enjoy about working on Daily POP Crosswords?

I love doing the research. I learn something new for every theme I do. I like that it’s a learning experience for me as both a constructor and a solver. This is quite different than traditional crosswords that rely more on wordplay.

Patti Varol is an amazing editor. Her insight makes me a better constructor. Also the volume of work she does is just staggering.

I love that the majority of constructors are women, although there are some great men as well.

I also solve the puzzles on Daily POP Crosswords every day. They are simple enough for any level but they all give an “Aha Moment” when I solve them.

Is there a particular theme day that appeals to you most or that you enjoy working on?

I enjoy sports themes the best. I’m a big fan of all sports and I’m an enthusiastic spectator. Football is probably my favorite sport.

When I do Book Smart themes, it introduces me to books I hadn’t thought much about and has led me to read new books.

I enjoyed learning new things about David Bowie in an upcoming puzzle I made. But the downside is a particular song keeps playing in my head. (But I won’t say which one, because it’s a spoiler.)

A huge thank you to Bonnie for her time! Be sure to keep your eyes peeled for her puzzles in the Daily POP Crosswords app, free to download for both iOS and Android users!

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!

# Super Bowl Snack Puzzle: The Solution!

Last Friday, we shared a football-themed brain teaser just in time for Super Bowl Sunday, and today, we’re going to walk you through solving it!

So, first, let’s refresh you on the puzzle itself:

Five couples have gathered for the big game, each football-loving woman having invited a male date, because it’s fun to invert stereotypes sometimes.

The women are Amanda, Evelyn, Janice, Rhianna, and Sue, and the men are Bill, Cory, Mack, Ted, and Walter.

Each couple brought a different snack: Doritos, Pringles, Lays, Tostitos, and Cheetos.

Can you figure out which couples brought which snack from the hints below?

1. Ted did not accompany Rhianna to the Super Bowl party.
2. Amanda and her date brought Doritos to the party.
3. Bill and his date and the couple who brought Pringles cheered for the Falcons.
4. Rhianna and her date cheered on the Patriots.
5. Mack and his date decided to bring Cheetos.
6. Evelyn and her date did not bring Lays chips.
7. Sue and her date, who wasn’t Ted, were Patriots fans.
8. Sue and her date didn’t bring Tostitos.
9. Cory and his date did not bring either Lays or Pringles to the gathering.
10. Bill and Amanda and their dates all sampled the five different types of chips.
11. Evelyn and her date did not bring Tostitos.
12. Ted and his date cheered the halftime show instead of either team.

So, given all the information, we know there are five couples, and we have clues regarding the men, the women, the snacks, and what they were rooting for. Let’s build a grid to help organize our information.

With the info in Clues 2, 3, 5, and 10, we have this starting grid:

We can now start to map out where some of the other women fit. According to Clues 4 and 7, both Rhianna and Sue were Patriots fans, which means they weren’t part of couples 1, 2, or 3.

Now, this doesn’t immediately place Sue or Rhianna, but when you combine this information with Clue 12, we can place Ted.

If we turn our attention to Clue 9, we can now place Cory, since we know he and his date didn’t bring Pringles or Lays, which means he can only be part of couple 5.

Since he didn’t bring Lays, we can also place both Lays and Tostitos in the snack column. And, by placing Cory, we also place Walt in the men column.

According to Clues 8 and 11, neither Evelyn nor Sue brought Tostitos, so we can place Rhianna in couple 5 with Cory. That leaves Sue as the other half of Patriots-cheering couple 4.

Finally, Clue 6 tells us that Evelyn didn’t bring Lays chips, meaning that we can place her in couple 3, and Janice in couple 2, completing our grid.

And there you have it, five couples enjoying the big game (or the halftime show). To each their own.

How did you do, fellow puzzlers? Did you unravel this one in celebration of Game Day? Let me know how you did!

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!