The Next Die
Which die completes the following sequence:
SOLUTION
If you look at dots in the top row, you will see that they are put together into groups of 1, 2, 3, 4, and so on.
Category: Brain Teasers
A collection of Math, Chess, Detective, Lateral, Insight, Science, Practical, and Deduction puzzles, carefully curated by Puzzle Prime.
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Ten Lanterns
You have ten lanterns, five of which are working, and five of which are broken. You are allowed to choose any two lanterns and make a test that tells you whether there is a broken lantern among them or not. How many tests do you need until you find a lantern you know for sure is working?
Remark: If the test detects that there are broken lanterns, it does not tell you which ones and how many (one or two) they are.
SOLUTION
You need 6 tests:
(1, 2) → (3, 4) → (5, 6) → (7, 8) → (7, 9) → (8, 9)
If at least one of these tests is positive, then you have found two working lanterns.
It all of these tests are negative, then lantern #10 must be working. Indeed, since at least one lantern in each of the pairs (1, 2), (3, 4), (5, 6) is not working. Therefore, there are at least 2 working lanterns among #7, #8, #9, #10. If #10 is not working, then at least one of the pairs (7, 8), (7, 9), or (8, 9) must yield a positive test, which is a contradiction.
Buffalo Buffalo Buffalo
The sentence below is grammatically correct. Can you explain it?
Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo.
SOLUTION
The sentence says that buffalo (animals) from Buffalo (city, US), which are buffaloed (intimidated) by Buffalo (city, US) buffalo (animals), themselves buffalo (intimidate) buffalo (animals) from Buffalo (city, US).
Diagonal in a Rectangle
A 1000 × 1004 rectangle is split into 1 × 1 squares. How many of these squares does the main diagonal of the large rectangle pass through?
SOLUTION
Notice that the number of small squares the main diagonal passes through is equal to the number of horizontal and vertical lines it intersects. Indeed, every time the diagonal goes through the interior of one square to the interior of another, it must intersect one of these lines.
There are 1000 + 1004 = 2004 lines which are intersected by the main diagonal. However, on four occasions (which is the greatest common divisor of 1000 and 1004), the main diagonal intersects one horizontal and one vertical line at the same time, which results in double-counting., so we must subtract 4 from the answer.
Therefore, the answer is 1000 + 1004 – 4 = 2000.
Rhombuses
A regular hexagon is split into small equilateral triangles and then the triangles are paired arbitrarily into rhombuses. Show that this results into three types of rhombuses based on orientation, with equal number of rhombuses from each type.
SOLUTION
Color the rhombuses based on their type and imagine the diagram represents a structure of small cubes arranged in a larger cube. If you look at the large cube from three different angles, you will see exactly the three types of rhombuses on the diagram.
Alternatively, the problem can be proven more rigorously by considering the three sets of non-intersecting broken lines connecting the pairs of opposite sides of the hexagon, as shown on the image below. The type of each rhombus is determined by the types of the broken lines passing through it. Therefore, there are n² rhombuses of each type, where n is the length of the hexagon’s sides.
Unravel the Rope
Is it true that for every closed curve in the plane, you can use a rope to recreate the layout, so that the rope can be untangled?
Said otherwise, you have to determine at each intersection point of the closed curve, which of the two parts goes over and which one goes under, so that there aren’t any knots in the resulting rope.
SOLUTION
Start from any point of the curve and keep moving along it, so that at each non-visited intersection you go over, until you get back to where you started from.
Blue and Red Points
You have 100 blue and 100 red points in the plane, no three of which lie on one line. Prove that you can connect all points in pairs of different colors
SOLUTION
Connect the points in pairs of different colors so that the total length of all segments is minimal. If any two segments intersect, you can swap the two pairs among these four points and get a smaller total length.
Petals Around the Rose
This is a puzzle that is best played with friends and real dice on a table. The rules require one of the players to throw 5 dice at once, and then answer correctly “how many petals there are around the rose”. The procedure gets repeated until everyone has discovered the secret rules of the puzzle or has given up.
How many throws do you need in order to figure out this classic puzzle?
There are 6 petals around the rose.
SOLUTION
The roses are the middle dots on the dice, and the petals are the dots around them. Just count the number of all petals appearing on the five dice and you will get the answer. 1 -> 0, 2 -> 0, 3 -> 2, 4 -> 0, 5 - > 4, 6 -> 0.
Puzzle at the End of the Book
“Puzzle at the End of the Book” is a very challenging puzzle from the 2017 MIT mystery hunt. The answer to this puzzle is a 6-letter word, related to a woman’s beauty. The solution is intricate and requires careful analysis of the book, some geeky references, and possibly a good amount of Google searching. Use the hints below if you need help with solving puzzle.
Page 1 
Page 2 
Page 3 
Page 4 
Page 5 
Page 6 
Page 7 
Page 8 
Page 9
Source: MIT
HINT 1
Pay attention to the words in green. They form a riddle which needs to be answered.
HINT 2
Pay attention to the broken lines along the bubble speeches. Use an appropriate code to decode them.
HINT 3
Pay attention to the ship, the brick wall, the ladder, and the bucket. Use an appropriate code to decode them.
HINT 4
Pay attention to Grover’s arms. Use an appropriate code to decode them.
HINT 5
Pay attention to the fonts used for typing the words in red. Use their first letters to form a word.
HINT 6
Pay attention to the unusual words appearing in the text. Use parts of these words, combined with immediately preceding/succeeding parts of neighboring words, to get the names of six
HINT 7
The names of the six muppets have the same lengths as the six words discovered from the previous steps. See which letters overlap when you compare each muppet name with its corresponding word. Arrange these letters to get the final answer.
SOLUTION
The answer to this puzzle is MAKEUP.
In order to get to it, first you must find 6 secret fantasy related words.
1. The green words on the pages of the book form the sentence Wooden ship turned around before understanding sea monster (SIX). “Wooden ship” = ARK, “turned around” -> KRA, “understanding” = KEN, so we get KRAKEN, which is a sea monster with six letters.
2. The broken lines along the speech bubbles can be decoded using Morse code to spell Lilith, Morrigan, Scarlet, or Queen of Pain. These female demons give the secret word SUCCUBUS.
3. The ship, the brick wall, the ladder, and the bucket contain four hidden Brail letters, which spell out the word HUMA.
4. Grover’s arms encode through semaphore the Inuit mythological creature QALUPALIK.
5. The word “Puzzle” is written in five different fonts – Times New Roman, Impact, Twentieth Century, Arial, Nosifer. The first letters of these fonts form the word TITAN.
6. Each page from 2 to 8 contains some unusual words. Part of these words, combined with immediately preceding/succeeding parts of neighboring ones, give the six Pokemons Sandshrew, Pinsir, Ekans, Clefairy, Tentacruel, Eevee, Rapidash. Their first letters form the secret word SPECTER.
The names of the six muppets on the last page are Barkley, Donmusic, Elmo, Kermit, Misspigy, Oscar. They perfectly match in terms of length with the six secret words which we found above. Also, each pair of name with secret word overlap in just one position, the six resulting letters are E, U, M, K, P, A. If we arrange these letters with respect to the length of their corresponding words, we get the final answer MAKEUP.
Eight Queens Puzzle
Place 8 queens on a chessboard, so that no two of them attack each other. For an extra challenge, make sure that no three of them lie on a straight line.
SOLUTION
The original puzzle has 12 unique solutions, up to rotation and symmetry. With the additional restriction imposed, there is only one solution.
