Solution to ThinkGeek’s Preposterous Puzzle

Here is the my solution to the puzzle:

Warning: Continue reading ONLY if you have already tried and really want to see the solution to ThinkGeek’s preposterous puzzle. I won’t post an image of the solution because I do not want people to see it by mistake.

Solution:

– Start with the original configuration of the picture below. I will refer to the pieces by the numbers in this picture:

– Exchange the positions of the two triangles 1 and 5. They are almost the same size so this step should be possible.

– Take out the pieces 2 and 3.

– Place the piece 6 (the little square) so that it touches both the pieces 1 and 4.

– Place the piece 3 so that it touches the pieces 4, 5 and 6. There are only two ways to do this and only one of them makes sense and determines how to place the remaining piece 2.

Have doubts about this solution? Comment below! :)

Set (Card Game)

I’d first like to apologize for not writing any new posts in the last few days. I’ve been too busy having lots of fun 200 miles away from home. I have received a lot of traffic lately, most of it by people searching for the solution to ThinkGeek’s preposterous puzzle (check out my previous posts: this one and then this one). I promise to post the complete solution as soon as I get mine, but for now enjoy my very short review of Marsha Falco’s highly entertaining card game Set.

In this real-time game, cards are laid down on the table and players are challenged to find and withdraw groups of three cards (called sets) that satisfy some special conditions. Check out Wikipedia’s article for the exact rules and some variations of the game. This game is highly addictive and competitive. It is recommended for two or more players but it can also be used to test your own abilities by challenging yourself to find the largest number of sets in the shortest time possible. A few difficult (well, at least some of them) exercises for those of you who have some math background are the following:

How many different sets exist?

How many different sets exist that contain one given card?

How many cards may be laid down without creating a set?

In how many ways can the complete deck (of 81 cards) be partitioned into 27 sets?

What is the probability that three randomly chosen cards form a set? (notice that this question can be answered using the first one). Now, what if you randomly select 6 cards from the deck, what is the probability that it can be partitioned into two sets? What if you choose 9 cards? 12? 15? …

As I said, these questions are mainly for math geeks like me (though the game is for everyone!), but anyone who can understand them may be able to try them. Some of these have already been answered on the web. Just Google them or comment below if you wish to know the answers. Have fun!

How to create your own crossword puzzle online

I know this blog is supposed to feature puzzles for your enjoyment rather than tools to make your own puzzles but ArmoredPenguin.com’s crossword puzzle generator is too good to ignore it. There are many puzzle generators on the web but this is the only one I have seen with so many options. There is also a wordsearch puzzle generator and other eduactional tools.

A Math Game: Fun and Simple

I don’t know who invented this game so if you know it please comment below and let me know so I can cite the source. I think I first saw it on a Spanish TV show from the network TVE.

The players are given a sequence of numbers and a target, for example:

1, 1, 2, 13, 25 → 20

(the target here is 20)

The goal is to produce the target number using only the sequence of numbers and basic mathematical operations (addition, subtraction, multiplication and division). Brackets (parentheses) can be used as much as needed. For example 1×((13+25)÷2)+1 is a solution to the puzzle above. Another solution is (25+13+1+1)÷2. Notice that it is required that each number is used exactly as many times as it appears in the sequence.

This is one of the few puzzles which you can create yourself in a second and still be almost sure it has a solution as long as you add a couple of small numbers to the sequence. And even when it doesn’t have a solution, it is a nice challenge to get as close to the target as possible. On the Spanish tv show the winner was whoever found the exact number first or the one with the best approximation when the time was over.

Below are some puzzles, all of which have at least one solution. Write your comments and solutions in the comment section and let us know if you have more puzzles :). Have fun!

1, 3, 12, 13, 23, 54 → 99

2, 4, 5, 10, 81 → 18

3, 9, 23, 23, 45 → 17

16, 25, 43, 80, 90 → 1

20, 41, 62, 83, 100 → 66

4, 6, 21, 32, 44, 60 → 12

The Ken Ken Puzzle Craze

As you have probably guessed, KenKen puzzles have nothing to do with Barbie or Street Fighter. They are a relatively new kind of mathematical puzzle similar to Sudoku, developed last year by a rather unorthodox Japanese Math teacher named Tetsuya Miyamoto.

An unsolved KenKen puzzle looks something like this:

A 6x6 KenKen Puzzle

Since this is a 6×6 puzzle (there are also 4×4 and 8×8 KenKens), every row and every column must contain the digits from 1 to 6 in some order. Notice that each one of the heavily outlined cages has a target (a number) and an operation assigned to it. These parameters can be seen at the top-left corner of each cage. The numbers occupying the cells of a cage must produce its target after being combined in some order using its operation. A cage consisting of only one square doesn’t have an operation and must simply be filled up with its target. Here is an example of a finished 4×4 KenKen puzzle:

A Finished 4x4 KenKen Puzzle

Check out KenKen.com for more information and puzzles.

Online Jigsaw Puzzles?

Do you love jigsaw puzzles but are terrified by the thought of losing a piece? (cue dramatic music) Then justjigsawpuzzles.com, jigzone.com and flash-gear.com/puzzle/ are the places for you (happy music). All three work pretty much the same and you won’t find much more on the web. An extra feature on justjigsawpuzzles.com allows you to create your own puzzle from an uploaded image, while flash-gear.com/puzzle/ works only with uploaded images. Another [quite strange] jigsaw game is Jigsaw Deluxe.

I understand how someone as compulsive as I am would love these websites but I normally prefer playing more sophisticated puzzle games that take advantage of the graphical possibilities of modern technology. A few addictive suggestions (which have very little or nothing to do with jigsaw puzzles) follow:

3D Logic (scroll down to see the game).

Sloyd.

Bloxorz.

Planarity.

I’ll add others when I remember more games. Don’t forget to come back to The Hourly Puzzle :)

Knights and Knaves Puzzles

Knights and knaves puzzles were first formally introduced in Raymond Smullyan’s book What is the Name of This Book?: The Riddle of Dracula & Other Logical Puzzles. I won’t go too deep into their history as you will easily find that in many other sources.

The setting for these puzzles is an island, all of whose inhabitants are either knights or knaves. Knights always tell the truth (they never lie), while knaves always lie (they never tell the truth). A knights and knaves puzzle typically consists of a challenge to make a logical deduction based on the simplicity of the setting. I’ll explain myself better through some examples:

The following are the two basic examples found on Wikipedia and other web sources. John and Bill are residents of the island:

First example: John says “We are both knaves.” What are John and Bill?

Second example: John says “We are of the same kind,” after which Bill says “We are of different kinds.” What are John and Bill?

Testing all the four possible cases provides us with the answers to each of the two puzzles above. In the first one for example, the only possibility is that John is a knave and Bill is a knight. The second one also has only one possible solution which I will leave for my readers to figure out.

The most famous of all knights and knaves puzzles is much more difficult than the two examples above: At some point in your trip through the island, you are forced to choose between two doors, one of which is guarded by a knight while the other one is guarded by a knave. One of the doors leads to instant death while the other one allows you to continue with your tour. You don’t know which door is which, or which guard is which. You must make one (and only one) yes-no question to one (and only one) of the guards. After receiving the answer to your question, you must choose a door based on that answer. Which question would you ask and which door would you choose?

An even more difficult puzzle has been called The Hardest Logic Puzzle in the World, but for now I will just share with you some knights and knaves puzzles I came up with tonight. They may or may not be originally mine, but I devised them independently for this post. Andy, Bob, Carl, Dave and Evan are all residents of the island.

• Can you figure out Bob’s kind by asking one yes-no question to Andy?

• Can you figure out the number of knights among Bob, Carl, Dave and Evan by asking two yes-no questions to Andy?

• How many yes-no questions do you need to ask Andy to figure out the number of knights among the five of them?

Have fun solving them! Remember to post your comments, questions, solutions and related puzzles in the comment section below.

ThinkGeek’s Preposterous Puzzle Solved?

I have been getting a lot of traffic from people searching for the solution to ThinkGeek’s missing square puzzle so I have decided to interact a little bit with the searchers. I haven’t received my Preposterous Puzzle yet so I cannot give you exactly what you are looking for, but at least I can give you a basic idea. For most people this post will be completely useless but I might be able to provide a little help to some of you who have no idea how to start. As I said in a previous post, this puzzle is remarkably similar to the classic missing square puzzle (click here for the statement and solution of this classic puzzle), and its solution should be pretty much the same.

Once you have figured out (or read) the solution to the classic missing square puzzle, you are now open to the possibility of imperfections in the original arrangement of the Preposterous Puzzle. At first sight the pieces seem to fit perfectly without the square, but do they? If you look carefully there is at least one big hole between the largest piece and one of the triangles. This big hole is a rectangle whose width is about three times the side of the little square, and whose height is about one third the side of the little square. Basic math tells us that the surface of this hole is about the same as the surface of the little square, and that gives us hope that the puzzle can be solved.

My suggestion is to open your mind to the following facts:

• The largest piece may not be symmetric.
• You may be able to turn the pieces upside down (which is not necessary in the classic missing square puzzle).
• The original arrangement is not perfect.
• One of the obtuse corners of the large piece seems to be chopped off (I don’t know if this is useful).
• The pieces should fit perfectly with the little square, so if you are trying an arrangement and you are leaving holes, you might want to start again and try another approach.

Ok so it turns out I was wrong about some of the points above being useful for the solution to the puzzle. Read my most recent post about this puzzle for the actual solution! :)

The Preposterous Puzzle

Read also the newer post: ThinkGeek’s Preposterous Puzzle Solved?

Many of you have already seen the lateral thinking puzzle commonly known as the missing square puzzle. It seems at first to be a paradox but it has a simple (yet far from obvious) solution. The first figure below seems to have a larger surface than the second since the second one is missing a square. However they are both formed by the same set of pieces. Can you explain what’s going on?

The Missing Square Puzzle

Once you have solved (or seen the solution to) this puzzle, you may wish to check out ThinkGeek’s real life variation of the missing square puzzle, the Prepousterous Puzzle.

Welcome to The Hourly Puzzle Blog

Welcome my dear visitors! I have just started this blog a couple of days ago and without any kind of advertising I already got more visits than I would have expected (which is nice!). However, aside from one funny spam, I haven’t received any comments or answers to my puzzles so far (I know, I must be patient…), so I thought I would encourage you readers to write whatever you feel like writing! So far I have posted a couple of puzzles (one of them is original!) and I invite you to read them and give me your opinions (or solutions!) on this early content. I would be specially grateful if you give me your thoughts on the direction this blog should follow in the near future. I aim to provide you with the funnest possible (original and borrowed) content in the world of brain teasers and puzzles in general, but for now I wish to hear from you! This message will remain on top for a few days but more content will be posted below so keep coming for more! You may or may not be disappointed :)