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XKCD is one of the most successful comics online of all time. Marketed as a “webcomic of romance, sarcasm, math, and language”, it manages to poke fun at all of these in various highly creative ways. Due to its numerous STEM references, XKCD is appreciated especially by geek communities. You can see one of our favorite strips below, a clever joke about classic chess puzzles.
To get to the XKCD website, simply click the image below.
What is the product (x – a)(x – b)…(x – z) equal to?
This product is equal to (x – a)(x – b)…(x – x)(x – y)(x – z) = 0.
Consider a chess game in which every player is allowed to move twice per turn. Show that Black does not have a winning strategy.
Assume Black has a winning strategy. Then if White plays Kb1-Kc3 and Kc3-b1 on his first turn, the game basically will start all over again, but with Black moving first. Therefore White will have a winning strategy, which is a contradiction.
Two moms, Sarah and Courtney, are talking to each other.
Sarah: I have two children
What is the probability that both of Sarah’s children are boys?
Courtney: Me too! Do
What is the probability that both of Courtney’s children are boys?
Sarah: Yes, I do! What is your younger child?
What is the probability that both of Sarah’s children are boys?
Courtney: It is a boy. He is so mischievous!
What is the probability that both of Courtney’s children are boys?
Sarah: Is he Sagittarius? Sagittarius boys are known to drive their mothers crazy. I can testify from personal experience.
What is the probability that both of Sarah’s children are boys?
Courtney: No, but actually I have the opposite personal experience to yours.
What is the probability that both of Courtney’s children are boys?
Sarah: Well, I guess astrology does not always get it right.
Courtney: I assume it does about half of the time.
The answers are: ~1/4, ~1/4, ~1/3, ~1/2, ~23/47, 1.
Explanation:
Initially, we do not have any information about the children and therefore the chance that both of them boys is 1/2 × 1/2. This applies to the first and the second question.
After Sarah says that she has at least one boy, there are equal possibilities that she has Boy + Boy, Boy + Girl, or Girl + Boy. Therefore, the chance that both children are boys is 1/3.
After Courtney says that her younger child is a boy, the only remaining question is what is the gender of her older child, and therefore the chance is 1/2.
The fifth exchange implies that Sarah has a Sagittarius boy. There are 23 combinations such that both children are boys and at least one of them is Sagittarius. There are 47 combinations such that at least one of the children is a Sagittarius boy. Therefore, the chance that both children are boys is 23/47.
Finally, Courtney says that her younger child, which is a boy, is not Sagittarius, but her personal experience with Sagittarius boys is positive. Therefore, her older child is a Sagittarius boy and the chance is 1.
Which number must be written in the place of the dots?
Remark: The missing number does not necessarily have 3 digits.
If you turn the paper around, the text will read:
… = 19969 + 68199
99106 = 18108 + 80998
Therefore, the missing number is 88168, which after 180 degrees rotation becomes 89188.
Our second giveaway is over. Congratulations to the winner, M M Del Rosario, and to his nephew, who will have countless hours playing with all the wonderful toys we chose for him from Fun.com!
For our July giveaway, we are partnering with our friends at Fun.com, a great website for games, toys, and fun Halloween costumes. We have prepared for you a colorful picture with lots of hidden stars in it. Answer correctly what their number is and on the 15th of July, you could be the lucky winner who gets more than $100 worth of puzzles and games, including “Perplexus”, “Codenames”, “Manifold”, and many more!
UPDATE: The game Brandscape is not active anymore.
Here is a nice pop-culture puzzle quiz by our friends at Funding Circle. They have created a colorful painting with 60 hidden references to famous brands in it, which you must find and recognize correctly. The puzzle is fiendishly hard but really fun to solve. To play it, just click the image below
Our first puzzle contest is officially over. Congratulations to the winner Kuan L.!
Also, special thanks to Rajesh Kumar, Johann Sturcz, Dave Phillips, P. A. Heuser, as well as ThinkFun and Dover Books for contributing puzzles.
Time for work – 1 hour
1. Connections
Examine the diagram and find which pairs of letters are connected with each other.
2. King Kong’s Maze
Detective Roy Omoshi (upper right) is chasing a dangerous criminal (lower left) through a destroyed maze. King Kong is trying to help Roy by putting together all the pieces of the maze
3. Color Path
Enter by the bottom red path and exit from the top of the maze. You may retrace your path, but you may not make a U-turn on a pathway. You must follow the paths in the order red, blue, yellow, and then red, blue, yellow again, changing color at the white squares.
4. Amy’s Cats
Aunt Amy’s six cats have sat around the carpet, next to the thread, the pot, the cage, the coffee, the shoes, and the aquarium. You know that:
Find the names of the cats clock-wise around the carpet, starting from the left.
5. Chess Connect
The starting and ending positions of 7 chess pieces are shown on the board. Find the trajectories of the pieces, if you know that they do not overlap and completely cover the board.
Notes: The pieces can not backtrack. Two trajectories can intersect diagonally but can not pass through the same square. Only the Knight’s has a discontinuous trajectory.
6. Sheep and Wolves
A shepherd takes his two sheep every day to a 7×7 lawn, so that they can eat the fresh grass there. However, there are five wolves on the lawn which are preying on the poor sheep. The shepherd decided to build a closed, non-intersecting fence around the sheep, so that all wolves end up on the outside. He planned the shape of the fence carefully and installed several signs showing the number of fence pieces around the corresponding cells. Can you figure out the shape of the fence the shepherd is going to build?
Solutions
Our first puzzle giveaway is over. The winner, Ankush S., is not living in the US, so he decided to donate his prize to a children’s home in Illinois! As an appreciation for his gesture, we created one of our signature avatars for him. Congratulations!
Solve the puzzle below and post the answer on our Facebook page, for the chance of winning the puzzle game Cat Crimes, provided by our friends at ThinkFun.
On the image below you can see 11 points in the plane placed in such
CAT = 3, BOWL = 2, FISH = 1. The scratches represent Roman numerals.
4 (CAT with a FISH) + 6 (VI) + 2 (TWO FISH) = 12
1 (FISH) + 2 (BOWL) + 5 (CAT with a BOWL) = 8
5 (CAT with a BOWL) + 3 (CAT) + 3 (III) = 11
Therefore, the correct answer is 4 + 2 + 3 = 9.
A square has dropped on the ground and broken into ten pieces. Accidentally, an additional, eleventh piece has fallen among the others. Can you figure out which one it is?
The total number of the squares in all pieces is 70 = 8 * 8 + 6. Therefore the extra piece is the one consisted of 6 squares.
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