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!

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!

Our Annual TableTop Tournament Starts Next Week!

With International TableTop Day fast approaching, we are once again teaming up with our pals at Penny Dell Puzzles to put together an in-house TableTop Tournament to celebrate the upcoming holiday (Saturday, April 27).

It’s a 12-person two-week tournament with different games to play every week, and round 1 kicks off next Tuesday. (This is actually the fourth year of the tournament, with all three previous champions competing again this year.)

One of the things I like about the layout of the tournament is that there are no one-on-one match-ups until the final. Instead of a single-elimination tournament, competitors are slotted into groups of three. Each group of three will play two games, and the two winners (one from each game) from each trio and move on to the next round.

So to survive round 1, I’ll need to win either Timeline or On the Dot.

Timeline is a card game where every card depicts a different moment in history, and the players are trying to place cards from their hand into a historically correct timeline. Players take turns adding cards to the timeline, placing them before or after previously played cards. You don’t have to know the exact year the event on a given card took place; you simply have to figure out when it happened in relation to the other events that have already been played.

You play your card, and then flip it over to reveal the actual year the event occurred. If you’re correct, the card stays, and you have one fewer card in your hand. If you’re wrong, the card is removed from the timeline and you draw a new card. The first player to place every card in their hand wins.

On the Dot is a pattern-matching game. Each player has four clear cards with randomly placed colored dots on them, and it’s up to the player to arrange all four cards so that the colored dots showing match a given pattern. The first player to match three patterns moves on to the next round.

Timeline can be a bit of a crapshoot, depending on your knowledge of a given subject and whatever cards you draw. I suspect I’ll have a better chance of making the second round with On the Dot; I’m fairly quick with pattern recognition and manipulation, and actually won three games in a row last year to secure my spot in the next round. Hopefully I can repeat the same feat this year.

But you never know. With new competitors and returning champions in the tournament this year, there are sure to be some diabolical surprises.

Here’s hoping when it’s all said and done, I’ll be wearing the Game Geek crown and holding the scepter high…


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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!