# Questions tagged [combinatorics]

A puzzle based on combinatorics, which is the study of counting discrete structures.

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### Table tennis tournament

Each of the five teams A, B, C, D, E consists of five table tennis players. In their tournament last week, each player has played one match against each of the twenty players in the other four teams. ...
1k views

### The juggling magician

In the magical circus, today a magician juggles with balls, cones, rings and umbrellas. While performing his art, he sometimes applies a powerful magic word: Ebrecedebre transforms one ball ...
943 views

### Five professors and nine dishes

Here's yet another puzzle adapted from a puzzle book (in my case, with edits to make some of the specifications of the puzzle more clear because I didn't really understand them the first time I read ...
860 views

### Rotationpuzzle in hex - The journey beyond the tomb

This is the 3rd themed puzzle of the tomb. (See puzzle 1 and puzzle 2) It is fully independent of the other two and just linked by the common story. After you set the colour-puzzle dials to the right ...
652 views

### Secret within the Gossiping Partiers

Al and Jane are hosting a party tonight. Al plans on proposing to Jane, a secret only he knows. The party begins and all 8 guests arrive on time. Immediately and again every minute, everyone forms ...
902 views

### Does this grid puzzle with a symmetry-breaking condition have a solution?

Since challenge questions are up in the air, what better time to pose a puzzle-building question that's intrigued me for some time. Preamble Consider an infinite square grid made up of nodes and edges ...
2k views

### Random Walk on Ring City

Ring City has 100 houses arranged in a circle. Alice starts at her own house, and every day she randomly moves to one of the two adjacent houses, each with 50% probability. She repeats this until she ...
768 views

### Counting numbers with 3 dice

Yesterday I saw a pair of calendar dice that can be rotated and swapped to show all days of a month between 01 and 31. The dice have a digit painted on each face. First die: [0, 1, 2, 3, 4, 5] ...
951 views

### Counting triangle algorithm

There is a type of puzzle where one needs to count triangles in a figure, generally a large triangle full of lines which create smaller ones. One example Is there, or can someone develop ;), an ...
3k views

### Coin weighing with a single weighing device

You have 12 coins which each weigh either 20 grams or 10 grams. Each is labelled from 1 to 12 so you can tell the coins apart. You have one weighing device as well. At each turn you can put as many ...
1k views

### Nerds, Jocks, and Lockers

Here's an oldie but goodie from The Daily WTF; I paraphrase to avoid copyright issues: A middle school math teacher, who also happened to be the P.E. coach, made the following deal with the non-...
1k views

### Automatically a Knight, Knave, and Joker

Let M be a finite positive integer. It's exact value is not known. Suppose we have three classes of automaton, all of which accept a bit stream as input, produce a bit stream as output (one bit per ...
572 views

### How many Jellybeans are in the bottle

There are $n$ jellybeans in a bottle with unknown dimensions. What is the only surefire way of knowing how many jellybeans are in the bottle?
431 views

### Every tournament has a dominant player

A tournament was played round-robin: each pair of players played a match where one defeated the other. Prove that there was a player for which every other player either lost to them or lost to someone ...
1k views

### N-dimensional Tic-Tac-Toe variant

Consider the game surface to be an infinite N dimensional Cartesian lattice. The rules are X moves first, but O gets to move ...
8k views

### A King and his Servants [duplicate]

A king sent 10 of his servants out to buy him each 10 gold rings. Each ring should weigh 10 grams, and altogether there should be 100 gold rings. One of the King's spies told him that one servant had ...
1k views

### The Monster Garden

You are the praetor of Tri, a small triangular-shaped nation bordered on the northwest by the Kingdom of Sauria, on the northeast by the Sultanate of Avia, and on the south by the Republic of Cryosta, ...
2k views

### How Many Times will 1 Appear on the Broken Clock?

You just got a new clock, but it's broken. Your friend tells you he can fix it, but he needs a little bit of data from it. One thing he needs is how many times 1 appears in the run of 2 days. The ...
4k views

6k views

### Two spies throwing stones into a river

There is a puzzle about two spies: Two spies must pass each other two secret numbers (one number per spy), unnoticed by their enemies. They have agreed on a method for doing this using only 26 ...
10k views

### N balls and a scale

The question of twelve balls and a scale is probably the best-known example of the "find the ball of a different weight" problem. But does it generalize? Is there a general way to find a weighing ...
23k views

### What's the fewest weights you need to balance any weight from 1 to 40 pounds?

Suppose you want to create a set of weights so that any object with an integer weight from 1 to 40 pounds can be balanced on a two-sided scale by placing a certain combination of these weights onto ...
95k views

### Twelve balls and a scale

You are given twelve identical-looking balls and a two-sided scale. One of the balls is of a different weight, although you don't know whether it's lighter or heavier. How can you use just three ...