Freezes When Overheated
What freezes when it is overheated?
SOLUTION
The answer is COMPUTER.
Difficulty: Advanced
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Beautiful Tapestry
A piece of a beautiful tapestry is missing. Can you figure out what its colors are?
SOLUTION
The tapestry represents the factorizations of the numbers from 2 to 26.
Each 12×12 square on the tapestry represents a number between 2 and 26, such that all squares representing prime numbers are painted in single colors. The colors of the squares representing composite numbers are determined by the factors of these numbers.
The number 2 is represented by orange color (top left corner). The number 3 is represented by green color. The number 4 = 2×2 is represented once again by orange (2, 2) color. The number 5 is represented by red color. The number 6 = 2×3 is represented by orange (2) and green (3) colors. The number 7 is represented by blue color. The number 8 = 2×2×2 is represented once again by orange (2, 2, 2) color. The number 9 =3×3 is represented once again by green (3, 3) color. The number 10 = 2×5 is represented by orange (2) and red (5) colors, and so on.
Murder Mystery Puzzles
In the three murder cases below, you can read the testimonies of all suspects. For each case, find who the killer is, knowing that no 2 people are in the same row or column, and that the killer was alone in a room with the victim.
EASY 
MEDIUM 
HARD
SOLUTION
The solutions are shown below.
Self-Describing Number
Find all 10-digit numbers with the following property:
- the first digit shows the number of 0s in the number
- the second digit shows the number of 1s in the number
- the third digit shows the number of 2s in the number, and so on
SOLUTION
Let the number be ABCDEFGHIJ. The number of all digits is 10:
A + B + C + D + E + F + G + H + I + J = 10
Therefore, the sum of all digits is 10. Then:
0×A + 1×B + 2×C + 3×D + 4×E + 5×F + 6×G + 7×H + 8×I + 9×J = 10
We see that F, G, H, I, J < 2. If H = 1, I = 1, or J = 1, then the number contains at least 7 identical digits, clearly 0s. We find A > 6 and E = F = G = 0. It is easy to see that this does not lead to solutions, and then H = I = J = 0.
If G = 1, we get E = F = 0. There is a 6 in the number, so it must be A. We get 6BCD001000, and easily find the solution 6210001000.
If G = 0, F can be 0 or 1. If F = 1, then there must be a 5 in the number, so it must be A. We get 5BCDE10000. We don’t find any solutions.
If F = 0, then the number has at least five 0s, and therefore A > 4. However, since F = G = H = I = J = 0, the number does not have any digits larger than 4, and we get a contradiction.
Thus, the only solution is 6210001000.
FEATURED
Square Impossible
Take a square (or circle) coaster. Then, cut a hole in a piece of paper with the shape of a square, so that the side of that square is half of the side (or the diameter) of the coaster. Now, your goal is to push the coaster through the hole without tearing the paper (you can fold it).
SOLUTION
Coming soon.
Awkward Hidden Objects
Warning: this puzzle involves mature themes that are inappropriate for younger audiences. If you are not an adult, please skip this puzzle.
SHOW PUZZLE
Can you find the objects which are hidden in the images below?
SOLUTION
The solution is shown below.
FEATURED
Cheryl’s Birthday
Cheryl’s birthday is one of 10 possible dates:
May 15
May 16
May 19
June 17
June 18
July 14
July 16
August 14
August 15
August 17
Cheryl tells the month to Albert and the day to Bernard.
Albert: I don’t know the birthday, but I know Bernard doesn’t know either.
Bernard: I didn’t know at first, but now I do know.
Albert: Now I also know Cheryl’s birthday.
When is Cheryl’s birthday?
SOLUTION
If Albert knows that Bernard doesn’t know when the birthday is, then the birthday can’t be on May 19 or June 18. Also, Albert must know that the birthday can’t be on these dates, so May and June are completely ruled out.
If Bernard can deduce when the birthday is after Albert’s comment, then the birthday can’t be on 14th. The remaining possibilities are July 16, August 15, and August 17.
Finally, if Albert figures out when the birthday is after Bernard’s comment, then the date must be July 16.
Perfect Day
Dear Diary,
This morning, I woke up at 9 o’clock. My first job was to drink a glass of water and brush my teeth. After that, I ate an apple, 2 bananas, and a toast with almond butter for breakfast. Then, I went to the gym for one hour, took a shower, and came back home at eleven. I cooked a few pieces of chicken with sweet potatoes for lunch; ate everything. In the afternoon, I started working on my projects while listening to classical music. In the evening, I went for the 2nd time to the gym, did cardio for half-an-hour, and after that visited my friend’s apartment. We had together one big pizza for dinner and in the end, I fell asleep on his couch.
As you can see, my entire day was perfect, except that my laptop keyboard broke. Can you figure out what’s wrong with it?
SOLUTION
All of the numbers in the text are written using digit symbols except for the ones containing “one” (“one”, “eleven”, “first”). This inconsistency implies that the number “1” key on the keyboard is broken.
A Lady and a Cowboy
A lady and a cowboy lie next to a bullet, a dime, and a hook. As a result, someone is delighted but doesn’t show it. What are they doing?
SOLUTION
In Poker, the Queen is called “lady”, the King is called “cowboy”, the Ace is called “bullet”, the 10 is called “dime”, and the Jack is called “hook”. Thus, the poker player has a straight and that’s why he is delighted.
Monochrome Isosceles Triangle
All points on a circle are colored in blue and red colors. Show that you can inscribe inside the circle an isosceles triangle whose vertices have the same color.
SOLUTION
Inscribe a regular pentagon inside the circle. Three of its five vertices must have the same color, and they form an isosceles triangle.