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7
votes
1answer
2k views

What do these countries have in common?

The following alphabetical list contains independent countries with a certain common property. (The list is complete to the best of my knowledge). Australia, ???, Chile, Costa Rica, Cuba, ???, ???, ...
8
votes
2answers
473 views

Bumblebees and Honey bees

The current market price of 175 honey bees is more than the price of 125 bumblebees, but less than the price of 126 bumblebees. Is it possible to buy 3 honey bees and 1 bumblebee for altogether at ...
-1
votes
2answers
2k views

Longest alphabetical sentence [closed]

What is the longest alphabetized (by first letter) sentence you can construct? For example, consider these "words": be, a, fish, elephant, crashed, dead If this were a sentence, it would be valid:...
12
votes
3answers
3k views

Please help with this geocaching puzzle

Edit: added link for geocheck I have been working on trying to solve this puzzle for months and cannot come up with any solution. I have learned lots of puzzle solving methods in the process but I ...
5
votes
2answers
2k views

English words with the most consonants, all voiced or all unvoiced

What English words containing only voiced or only unvoiced consonants contain the most? Count each consonant as many times as it appears. Note that this is a question about the sounds (phonemes) ...
-5
votes
1answer
299 views

Looks like ECB — What story is this?

Secrets Revisited A friend sent me the following and wanted to find out if anyone could figure it out. The message was encrypted three times, and all keys and primers were provided. It appears that ...
5
votes
4answers
300 views

Yet another group of five sequence puzzles

This is my third batch of sequence puzzles that are nasty and hard to solve; yet, each of them has a clear and justifiable solution. Sequence 1: 2, 4, 4, 3, ?, ?, 3, 4, 2, 4, 3, 4, 2, 2, 3, 4, 4,...
13
votes
7answers
4k views

Fair n-sided dice

I have recently bought a fair $10$-sided dice for generating equally distributed random numbers from the range $1,2,\ldots,10$. Let me describe this dice in some more detail. Consider a regular 5-gon $...
23
votes
3answers
2k views

Gambling in a rigged casino

A well-known crooked casino is offering the following bet with a pair of (identically looking and indistinguishable) dice that both show the numbers $1,2,3,4,5,6$ on their faces. The first die ...
5
votes
1answer
854 views

Who's the next target?

Kenny's a serial killer and he likes to play games. To make his killing spree more interesting, he leaves clues for the detectives on his next victim. One day, the police station received a message as ...
4
votes
2answers
257 views

Goldbach Cryptarithm

As the apology for the mischievous problem about knights and knaves: PRIME PRIME + PRIME ------- NUMBER Yeah, this was inspired by the famous (or infamous) ...
-1
votes
3answers
768 views

The German's are Experimenting

Could I BE any more riddle. your holiday starts, forget happiness no out from these mates of no friendliness your past is what we think as space tortures, beginning to shrink follow the sheep of ...
6
votes
2answers
792 views

Exercise with a piece of code and x[2][5]

I was given this exercise to solve. It's beyond me, but important for me to solve this. The following piece of code is all the context I was given. ...
14
votes
1answer
2k views

Cutting three sticks

Cosmo plays the following (single-player) game with three wooden sticks: He first checks whether he can form a triangle from the three sticks (which means: whether the longest stick is at most as ...
7
votes
6answers
2k views

Knights and knaves at a party

On an island, all inhabitants are either knights or knaves. Knights always tell the truth and knaves always lie. No tribe is gender related and some people marry into a different tribe. When I ...
16
votes
4answers
989 views

Fifty-two genuine and two fake coins

In the country Borgonia, there are only two types of coins: genuine ones and fake ones. All genuine coins have the same weight, and all fake coins have the same weight. The weight of a genuine coin is ...
2
votes
5answers
856 views

Five further sequence puzzles

This is my second batch of sequence puzzles that are nasty and hard to solve; yet, each of them has a clear and justifiable solution. Sequence 1: 18, 17, 18, 22, 26, 35, 32, 32, ??, 38, ??, 52, ?...
10
votes
2answers
814 views

Polygon wrapping a cube

A polygon is folded to perfectly wrap a cube, covering all of its surface area with no overlap. Show that the polygon had at least two equal angles.
20
votes
1answer
3k views

Riddle: Who wrote this doctoral thesis?

Who wrote this doctoral thesis? Published: August 1960 Abstract: Subject responses are investigated to antemeridial comestibles in the 510 nm range. Verbal responses was elicited by a hobbit ...
10
votes
3answers
598 views

Arnie and Barney: When is Barney's birthday?

The following twelve statements were made on a certain day X during the last 100 years. At least seven of these statements were true on day X: Exactly one month from now it will be Thanksgiving. ...
9
votes
3answers
1k views

n - archers and many arrows

Suppose there are n archers in a standoff and want to kill each other until there is just one archer remaining. However everyone's chance of hitting (and thus killing) another archer is not fair. ...
16
votes
2answers
1k views

The Erasmus rook tour

Professor Erasmus has found a special way of moving a rook across a standard $8\times8$ chessboard that he modestly calls the "Professor-Erasmus-rook-tour". The professor claims that in this tour, ...
18
votes
2answers
1k views

A US English riddle: My name is a state that is not my state. When I am downtrodden, my oppressors take risks

I came up with this riddle a few days ago. It's my very first riddle, so it shouldn't be too hard to crack. The two hints are: My name is a state that is not my state. When I am downtrodden, my ...
7
votes
1answer
729 views

Smallest number of matchsticks for a 3D structure with 6 matchsticks at each vertex

Make an as small as possible three dimensional structure of matchsticks, all of which have equal length, such that the end of each matchstick meets exactly five other ends. A matchstick is not allowed ...
7
votes
5answers
1k views

Turn 16 into 25. You have 4 magic spells. Can you do it?

You have been given the number 16. You also have 4 magic spells. You have to use the spells to turn 16 into 25. Each spell changed your number a specific way, but the objective is never altered, you ...
13
votes
1answer
905 views

Ernie and the Calendar

I had taken an extended summer break over the Christmas New Year period but finally returned to the city at the end of January, feeling relaxed and tanned. I was looking forwards to getting back in ...
13
votes
2answers
794 views

Lagrange's Four Square Cryptarithm

The French mathematician Lagrange proved that every natural number can be written as the sum of four squares. This is true in the view of cryptarithms, too. ...
8
votes
1answer
286 views

The Erasmus tedrahedron

Professor Erasmus has constructed a special tetrahedron that he modestly calls the "Professor-Erasmus-tetrahedron". The professor claims that all four faces of his tedrahedron are right-angled and ...
7
votes
2answers
2k views

A list of 100 statements

I was working my way through some puzzles in Discrete Maths by Rosen, when I came across the following question: The $n^{th}$ statement in a list of 100 statements is : "Exactly $n$ of the ...
5
votes
1answer
620 views

Scrambled Songs

I've used quite a simple algorithm to create the appearance of a jumbled up bunch of letters. These letters represent a song. What is the song title? TTLSHIWWYAUATWSHLADITSTTLSHIWWYA (Everyone ...
3
votes
2answers
348 views

Product and Sum, Variant 2b

My friends Peter and Sam are excellent mathematicians and always think strictly logical. Yesterday I told them: "I have secretly chosen two integers $x$ and $y$ with $1\le x\le y\le 99$. I have told ...
26
votes
3answers
5k views

How do I convince my grandmother?

How do I convince my grandmother (who really hates mathematics) that there exist three positive integers $x,y,z$ that satisfy the equation $28x+30y+31z=3650$?
5
votes
3answers
826 views

8 chess players in a round robin tournament

Eight people played chess in a round robin tournament. No match ended in a tie and both A and B won the first place. Since C and D were rivals, C beat all players who beat D and D beat all players ...
10
votes
4answers
2k views

Five sequence puzzles

The following five sequence puzzles are quite nasty and hard to solve. Yet, each of them has a clear and justifiable solution. Sequence 1: ?, ?, ?, B, B, C, ?, ?, F, ?, S, M, A, S, P, S, C, A, .....
23
votes
6answers
4k views

Fair share of a square watermelon?

One hot day, Stan, Kyle, and Kenny were sitting outside with a square watermelon (actually it was a cube like the picture below). Stan says "Let's cut the watermelon into 3 equal slices (like the ...
15
votes
5answers
2k views

Two genuine and two fake coins

In the country Argonia, there are only two types of coins: genuine ones and fake ones. All genuine coins have the same weight, and all fake coins have the same weight. The weight of a genuine coin is ...
8
votes
2answers
986 views

Ant on a rectangular box

An ant walks in constant steps from corner to corner over a rectangular box, always chosing the shortest path. From any given corner, the ant observes the shortest paths to the other seven corners all ...
17
votes
2answers
2k views

Classic “mathematical” riddle: 101 / 50 + 0 = 1/9. Who is it, and why?

I heard this classic riddle a long long time ago and really liked it, but I'm afraid it was way too simple for you all in the format that I originally heard it, so I have tweaked it just a little: ...
3
votes
2answers
282 views

Find seven points so any three contain two of distance one

Choose 7 distinct points in the Euclidean plane so that among any 3 of those points, there are (at least) 2 that are a distance of exactly 1 apart.
3
votes
4answers
24k views

Find length, width and height of a cuboid [closed]

Consider a cuboid (that is, a rectangular box / rectangular parallelepiped) with the following properties: the area of its top face is $240$ cm$^2$ the area of its front face is $300$ cm$^2$ the ...
3
votes
2answers
400 views

How many magazines?

You would like to sort some monthly magazines in different categories. Disregarding the title of magazines, there are 4 different categories if you arrange magazines by publishing year and month. ...
7
votes
1answer
950 views

Mousehunt cryptogram

I found this puzzle within the game Mousehunt It didn't seem to match any rune system that I know of. Rotating the image also didn't seem to show any useful information, although the first word when ...
11
votes
2answers
1k views

Filling chess pieces in smallest area

You have 2 bishops, 2 rooks and 2 knights (of no colour). Place them in as small a rectangle as possible such that each piece can be captured by atleast 2 other pieces in a single move. Bishops have ...
5
votes
2answers
525 views

Quick and dirty: painting a fence

There are four fences, which are geometrical identical (same heigth and same length). The following four people need the specified time to paint it: Bob needs 2 hours. Simon needs 3 hours. Tommy ...
10
votes
3answers
732 views

The Erasmus isosceles triangle

Professor Erasmus has constructed a special isosceles triangle that he modestly calls the "Professor-Erasmus-triangle". The professor claims that he can cut his triangle into three smaller triangles, ...
23
votes
1answer
4k views

Very simple, yet unsolved, sequence of numbers

A simple sequence of numbers, which I encountered during intermediate school, in my math book. Any person that finished intermediate school possesses the necessary toolbox required to solve this ...
13
votes
1answer
2k views

How to solve this 7x8 grid with partially and completely filled squares?

I've tried looking at the paper from different angles, and nothing is jumping out at me. I'm not sure what to try next. Thanks!
15
votes
1answer
2k views

Touching matchsticks with compass and straightedge

The question Touching Matchsticks asked for the smallest matchstick graph where every node is connected to four distinct edges. The Harborth Graph is the smallest such, with 104 edges connecting 52 ...
22
votes
1answer
2k views

Riddle - He who holds the answer may enter

Here's a riddle I used in a game some time ago. Not the best riddle ever, but we had fun solving it. It was written on a translucent door, on the frame of which was written "He who holds the answer ...
26
votes
5answers
3k views

A mathematician's coffee alphametic

Alfréd Rényi, a Hungarian mathematician, said that a mathematician is a machine for turning coffee into theorems. It's believed that his mention was about his colleague, Paul Erdős, the celebrated ...

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