# All Questions

22,598 questions
Filter by
Sorted by
Tagged with
512 views

### Magic back yards

My back yard forms a rectangular grid of squares except some of the squares are missing as they are covered by pipes or a small tree. The layout is as follows. A 'x' indicates a square that is free ...
2k views

### Miss Danner and the Elmer Boys

Miss Danner, a primary school teacher, is on her way to school - it's the first day of school this year. In class, she sees two identically looking boys sitting in the first row. Aw, twins, so cute!...
158k views

### Four prisoners wearing black and white hats

There are four prisoners. All four prisoners will be freed, if at least one of them correctly guesses the color of the hat on his head. They can't speak to each other, and they can't touch each other....
347 views

### What factors affect the difficulty of Hamiltonian puzzles?

There is a type of puzzle which can be modelled as finding a Hamiltonian path through a graph. One example is the Icosian game. What factors affect the difficulty of such puzzles, to be solved by ...
11k views

### Coin weighing problem

You are given ten stacks of golden coins, each stack consisting of ten coins and a digital scale with arbitrary precision. You know that all stacks of coins are made from gold, weighing 10 grams per ...
284k views

### 6, the magic number

Here's a fun (albeit difficult) one: Make these equations true using arithmetic operations: ...
609 views

### Pattern 1 — Numbers

Fill in the missing number: 10, 30, 60, 01,__, 12 Use a bit of lateral thinking. And math. Also, I do know the answer. Just giving the question as a teaser.
47k views

### Candle timing measurement [duplicate]

You are given two candles of equal size, which can burn 1 hour each. You have to measure 90 minutes with these candles. (There is no scale or clock). You are also given a lighter.
484k views

### Puzzle of putting numbers 1-9 in 3x3 Grid to add up to 15

In a 3x3 grid, I'd have to put numbers from 1 to 9 in a manner so that respective row, column and diagonal add up to 15. I have only been able to come up with one solution: 6 1 8 7 5 3 2 9 4 ...
654 views

Epimenides (a Cretan) once wrote a poem, in which he stated that all Cretans are liars. Since he is a Cretan, and therefore a liar, Cretans are veracious. But then again he wouldn't be a liar! This ...
1k views

### How to survive, with statistics

You are kidnapped and your offender plays a game with you. In front of you are 2 boxes, containing a total of 50 white balls and 50 black balls. The kidnapper will pull out a ball from one of the two ...
523 views

### Number of true sentences

You are given a sheet of paper with $100$ sentences, in the form of: There are exactly $x$ wrong sentences on this sheet. There is exactly $1$ wrong sentence on this sheet. There are exactly $2$ ...
662 views

### 3 Switches identification [duplicate]

Picture this. You are in a hallway of a very large office building. Near you are 50 light switches of which 3 are unlabled. These lightswitches are connected to 3 lights in 3 separate rooms. The ...
5k views

### The cage - a logic puzzle

One summer day John was jogging in the countryside wearing only his normal running clothes (shorts, vest, sports shoes and socks). After running for some time he saw that the lace of one of sports ...
636 views

### What's the largest number that can be obtained in the process of solving a numbers game on Countdown?

Countdown is a British game show in which people try and make the longest possible word out of nine given letters, reach a target number using six given numbers and basic arithmetic, and then solve a ...
4k views

### Spatial IQ test puzzles

The following puzzles were created by Robert Lato to measure IQ in range between 160 and 190. Whats the solution to them? You are supposed to draw in the dented boxes what the missing figure is for ...
2k views

### Is there a general strategy for decoding Brainfuck mutations?

There are many Brainfuck variations used in puzzles in geocaching, for example Ook! They are usually not so hard to decode because they are 'standards' - therefore the substitution is googlable, there ...
348 views

### How many subset intersections do you require?

Alice chooses a subset S of {A,B,C,D,E}. Bob makes a guess of any subset T and Alice tells him the number of elements in S$\cap$T. Bob has to continue making guesses until he can exactly determine S....
367 views

### Is there a second solution to points and perpendicular bisectors problem?

There is a problem from M.Gardner book ("Wheels, Life, and other Mathematical Amusements", p. 201): [Hallard T. Croft] asked if there existed a finite set of points on the plane such that the ...
431 views

### Land claim staking

It was traditional during the times of the Oregon Trail and the gold rush that men founding new towns were allowed to stake their claim on land upon arriving to the west coast. Suppose a man is ...
717 views

### Middle weight puzzle

There are 100 white and 101 black balls. All the balls have different weights. Balls of the same colour look the same. White balls are numbered from lighter to heavier (from 1 to 100). The same is ...
1k views

### Can anyone explain me how to solve this problem? [closed]

Two workers A and B manufactured a batch of identical parts. A worked for 2 hours and B worked for 5 hours and they did half the job. Then they worked together for another 3 hours and they had to do (...
7k views

### Remove first or last letter - What is the name of this word puzzle/type of word?

When I was a child I had a puzzle book. One of the puzzles involved finding words where you can remove one letter from the beginning or end of the word, and you still have a valid word. You can ...
7k views

### Who has mud on their forehead?

This is probably my favorite puzzle. It uses logic, but it's not one of those "logic table" puzzles which i dislike immensely. What is this type of puzzle called and are there more like it ...
595 views

### Find the smallest N to complete the task: “Write a true self-reflective statement about the digits from 0 to N”

Following this question, consider the case where we change the number of digits and formulate the task like this: Write the statement like "This statement contains $M_0$ 0's, $M_1$ 1, ..., $M_N$ N'...
770 views

### Write a true self-reflective statement about the digits from 0 to 9 (or prove it can't be done)

This statement contains 3 0's, 1 1, 4 2's, 1 3, 5 4's 92 5's, 6 6's, 53 7's, 58 8's, and 9 9's. Clearly that statement is incorrect. It only has 1 occurrence of ...
3k views

### A two-player game

This is from the current weekly math challenge from the newspaper Le Monde. Alice and Bob play the following game, in turn: A number between $1$ and $10$ is written on a blackboard. At each of their ...
1k views

### Most moveable chess position

What would be a chess position, where a player (white or black) has a maximum possible number of different moves to make? There are two options: 1. The position must be possible to obtain in a ...
2k views

### How can I spot an X-Wing?

I was doing a Sudoku puzzle (in my morning newspaper on the train to work) and got stuck at this point: ...
13k views

What is the solution for this puzzle from this IQ test?
7k views

### What is the pattern in this IQ test puzzle with spotted triangles and arrowed circles?

The solution for this test is 1. But what is the pattern? P.S. I checked that 1 is the answer by simply trying different options in the test itself (Russian site for the test is here: http://sly2m....
795 views

### What's the more general case of this puzzler?

There is a puzzle which I remember from many years ago which can be summarised as It is easy to arrange 20 items in five rows of four items, but how could you arrange just 10 items in five rows of ...
50k views

### Draw a line through all doors

I saw the following problem on 4chan and couldn't solve it: It's very likely to be some kind of troll (no solution). I'm hoping to see some rigorous proofs that disprove the existence of such a line....
3k views

### What is the smallest positive integer, which can not be written without repetitions of digits and using arithmetics only?

Suppose you are allowed to use all 10 digits (0,1,2,...9) at most once each; 4 arithmetic operations ($-$,$+$,$\times$,$\div$), each any number of times; parenthesises to group operations; and you can ...
2k views

Background Story A nomad is injured in the desert. And he can't move, but fortunately an oasis is nearby, and he can stay there for enough time until rescue arrives. But the water is a magical water, ...
499 views

### Drawing lines on a map

This was a puzzle that appeared in an old math contest as well as an unrelated puzzle book. Suppose we have a two-dimensional map with a lot of cities marked on it. For each city on the map, we ...
3k views

### To be a bookworm

I have a complete set of encyclopaedias on my bookshelf, beautifully bound and neatly arranged with volume 1 on the left and volume 32 on the right. They were a talking point when I bought them 30-odd ...
3k views

### How much red sand and how much blue sand?

This is a puzzle I remember arguing with my sister about when we were little... (Not quite as loud (or as public!) as the Monty Hall argument we had.) You have two large beakers of the same size. ...
930 views

### SuDoKu Unique Rectangles and the “2 blocks” rule

On HuDoKu's page on Uniqueness, under Unique Rectangle, it says A common mistake when looking for URs is to violate the "2 blocks" rule (see the Sudopedia article for an example). Unfortunately, ...
2k views

### Church charity lottery

Suppose you've rigged the church charity lottery so that you cannot lose (what a swell guy you are). There are 10 drawings, and you start off with 10 dollars exactly. At each drawing, you must chose ...
925 views

### Paying the unfair Troll toll

Here is more complicated Paying the Troll toll like puzzle: Between you and your destination, you have 7 bridges, and there is a troll under every bridge. Each troll, quite rightly, insists that ...
850 views

### How long is needed to clear the area of robots?

This question has been written in order to help answer Fastest way to collect an arbitrary army. There is a 1 x 1 square area with corners labelled clockwise A, B, C and D. A finite number of ...
456 views

### $N_{max}$ balls in 3 weightings

This is a small generalization of well known 12 balls puzzle: You are given two-sided scale and some number of balls. All balls have the same weight but one. It is of a different weight, although ...
2k views

### An arithmetic puzzle from 1645

The following problem is found in the first Norwegian arithmetic, published in 1645 by Tyge Hansøn: Three hundred oxen large and small, A cattle owner wanted to buy: 3 for 63 daler he got. ...
2k views

### I have a pattern problem to solve!

The question reads: From the given pattern, What comes in place of '?'
3k views

### Twelve balls on a scale, where one ball is lighter and another is heavier

Suppose you have twelve identical-looking balls. Ten of them are the same weight, but one is slightly lighter and one slightly heavier, in such a way that the weight of the lighter and heavier ball ...
254k views

### What is the number of the parking spot?

One needs to find the number under the car.
657 views

### Maximum time for ants to fall off stick (with a non-instant turning speed)

This question is purely a follow-up to Maximum time for ants to fall off stick. Suppose there are $n$ ants on a stick which has length 10. At any time, the ants may be facing left or right, the ...
Suppose there are $n$ ants on a stick which has length 1. At any time, the ants may be facing left or right, the initial directions of the ants are arbitrary. Each ant can be modeled as a point in the ...
This question is based upon the figure shown below.  \begin{array}{|ccc|c|ccc|c|ccc|} \; & 41 & \; & \; & \; & 31 & \; & \; & \; & ? & \; \\ 5 & \; ...