# 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!

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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!

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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!

# The UK Sudoku Championship: The Aftermath

This weekend, I sat down at my desk with a few sharpened pencils and a copy of the UK Sudoku Championship puzzles, ready to pit my puzzly skills against sixteen Sudoku and Sudoku variant puzzles.

According to UK Puzzle Association rules, I had two hours to complete as many puzzles as I could.

And let me tell you, my fellow puzzlers and PuzzleNationers, I don’t think I could have completed this entire packet in twice that time. The UK must feature some seriously impressive and speedy Sudoku solvers.

[If only I could puzzle with both hands like this brilliant youngster.
Image courtesy of Deccan Herald.]

Now, I’m by no means a weak Sudoku solver — deduction puzzles don’t faze me — but I’m not a fast Sudoku solver, so I knew the two-hour time limit was, at best, a pipe dream. Nonetheless, I set my timer, determined to give it my all.

The packet opened with a Linked 6×6 Sudoku, which was a pleasant starter. The two grids complemented each other nicely, and only needing the numbers one through six once per 2×3 box kept the solve quick.

That was not the case for puzzle #2, a Deficit Sudoku. In the Linked 6×6, you knew that the 2×3 boxes within the grid would contain the numbers one through six, which made it easy. In the Deficit Sudoku, the 2×3 boxes contained six numbers, but the options were numbers one through seven, so that certainly that came with puzzle #1 vanished instantly.

The Deficit Sudoku was certainly hard, and given that those two puzzles were only page one, my progress thus far didn’t bode well for the rest of the championship experience.

[A sample Deficit Sudoku.]

Puzzle #3 ratcheted up the difficulty with a Surplus Sudoku, one that featured boxes of eight squares in various shapes. Each box featured the numbers 1 through 7, plus one of the numbers again. If the design was to overwhelm the solver with possibilities, mission accomplished!

After laboring over the puzzle for a good twenty minutes or so, I had to move on without completing it. This would become a recurring theme in this puzzle packet.

Puzzle #4 was the elaboratedly named Odd-Even-Big-Small Sudoku, and although I got farther with this one than the Surplus Sudoku, I also had to bow out and move on after hitting the wall. This was page 2 of the championship, and it was a brutal step-up in challenge from page 1.

Puzzle #5 was a Classic Sudoku, obviously designed to restore a solver’s confidence after the one-two punch of Surplus Sudoku and Odd-Even-Big-Small Sudoku, and I knocked it out quickly. Huzzah! Back on track!

Puzzle #6 was also a Classic Sudoku, but one with desperately few set numbers. The upper-right 3×3 box and the lower-left 3×3 had NONE, and the upper-left 3×3 box and the lower-right 3×3 box only had two apiece.

Although I was able to fill the body of the grid quickly, those four corners had me stymied. For the third time in just over an hour, I put a puzzle aside unfinished.

That lack of set numbers was a recurring theme in the championship packet, making Puzzle #7 (a diagonal Sudoku) and Puzzle #8 (a Jigsaw Sudoku), much tougher solves than I expected. By this point, I put aside the timed aspect of the solve entirely (my two hours was nearly up, and I’d been interrupted a few times anyway), and just focused on doing my best to complete as many puzzles as possible.

This was about puzzly pride at this point. *laughs*

The next four puzzles — an Extra Regions Sudoku (where the shaded-in areas also contained the numbers 1 through 9), a Sum-Doku (or Killer Sudoku) with no set numbers, a Consecutive Pairs Sudoku with only eight set numbers, and an Odd Sudoku (with the shaded boxes requiring odd numbers only) — I’d categorize as tough, but fair.

I can see how a championship packet like this would separately the very good solvers from the truly great.

[A diabolical XV Sudoku.]

That was clearly the goal of puzzles #13 and #14. A Thermo Sudoku with only nine set numbers taxed me to my limit, and the XV Sudoku that followed was the hardest puzzle in the entire set. Admittedly, I was a little burnt out at this point, but it remains the toughest Sudoku puzzle I’ve ever attempted.

The final two puzzles, a Palindrome Sudoku and an Eliminate Sudoku, felt like a cakewalk compared to the gauntlet of challenging puzzles that preceded them. It was nice to close out my solving experience strong, nearly four hours into the challenge.

I fully intend to go back and take another crack at all the puzzles that bested me, but for now, I need a little break from these devious little grids.

Kudos to everyone who tackled the UK Sudoku Championship, and to some of the world-class contenders I saw on the final results board, I tip my hat to you all. The top nine finished all 16 with perfect scores in under an hour and a half! That is a blistering speed!

I may not have what it takes to be a UK Sudoku Champion, but I’m glad I accepted the challenge. It was a satisfying, intriguing, and occasionally humbling way to pass a few hours.

You can give the 2016 UK Sudoku Championship puzzles a shot yourself by clicking here. Good luck!

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# It’s Follow-Up Friday: ACPT View a Clue answers!

Welcome to Follow-Up Friday!

Follow-Up Friday is an opportunity to look back on past posts and puzzly topics. Whether we’re updating you with new developments, providing answers to a previously posted brain teaser or puzzle, or simply revisiting a subject with a fresh perspective, Follow-Up Friday lets us look back and look forward.

In today’s post, I’ve got the answers to last Friday’s pre-ACPT edition of the View a Clue game!

If you recall, we selected ten animals that commonly show up in crossword grids — some have become crosswordese at this point — to see if the PuzzleNation audience could identify them from pictures.

So, without further ado, let’s get to it!

#1 (3 letters)

Answer: GNU, also known as a wildebeest

#2 (4 letters)

Answer: LYNX, a wild cat native to the colder regions of the Northern Hemisphere

#3 (6 letters)

Answer: ONAGER, a wild Asian donkey-like animal

#4 (4 letters)

Answer: RHEA, a flightless South American bird

#5 (6 letters)

#6 (9 letters)

#7 (4 letters)

Answer: ZEBU, a humpbacked bull native to India

#8 (5 letters)

Answer: COYPU, a South American beaverlike rodent, also known as a nutria

#9 (4 letters)

Answer: KUDU, another type of African antelope

#10 (5 letters)

Answer: HYRAX, a rodent-sized relative of the elephant, native to Africa and Asia

How did you do? Let us know in the comments below!

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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