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votes
1answer
4k views

Confused about step 5 of official Rubik's 3x3 Cube solution

Solution guide: http://rubiks.com/uploads/general_content/Rubiks_cube_3x3_solution-en.pdf I can get to this point pretty reliably now, but when I try the method shown I'm just as likely to go from ...
3
votes
2answers
1k views

Unknown Consecutive Integers Puzzle

Two people, Anne and Bob, each hold an index card. A positive integer is printed on each index card, and these integers are consecutive (i.e. Anne's card may display 8 and Bob's card 7). Anne and Bob ...
22
votes
4answers
3k views

The Monty Hall problem

I'm amazed that, although well known, this problem hasn't been posted yet. Monty Hall You are on a game show. The host of the show shows you three doors. He tells you that behind one of them, is a ...
7
votes
4answers
2k views

Three 50/50 guesses

Three friends enter a quiz-show as a team, the final round of the show is all or nothing, they only get their prize if they can win this round. Three boxes labelled 1, 2 and 3 are placed in a room, ...
20
votes
3answers
5k views

The lake monster

You are on a rowboat in the middle of a large, perfectly circular lake. On the perimeter of the lake is a monster who wants to eat you, but fortunately, he can't swim. He can run (along the perimeter)...
9
votes
2answers
542 views

Generalizing the “shooting puzzle”

Inspired by this puzzle. You have $n$ shooters having a duel, labeled $1, 2, ... n$. Each shooter has an accuracy of $k_n$, with each $k_n$ some probability in $(0,1]$, with $k_1 < k_2 < ... &...
15
votes
1answer
2k views

Is this a new kind of liar puzzle?

I would like to ask if anyone has seen elsewhere this variation on the standard truth tellers/liars kind of puzzle. In the usual repertoire it is assumed that every person questioned knows the answer ...
3
votes
2answers
515 views

Find a high-scoring 53-digit prime number chain

Let a “number chain” be a series of numbers, $n_0, n_1, ... n_{m-1}$ for some $m$, such that in base 10 the low digits of $n_i$ match high digits of $n_{(i+1)mod m}$. For example, after the number ...
5
votes
7answers
6k views

Help understanding the solution to a “shooting puzzle”

I need help understanding the solution to the following puzzle: Puzzle: There is a "triangular" duel between the three shooters. Everyone shoots one by one, can shoot once and any person he wants. ...
3
votes
2answers
1k views

Find shortest network connecting four points

Given the figure below, find the shortest network of straight line segments (like a Steiner tree, or like parts of a Delaunay triangulation) that connects the four circled points while staying in the ...
2
votes
1answer
398 views

Make a wide tower of bridge-shapes

In this question, bridge stands for the illustrated convex quadrilateral, constructed from three equilateral triangles. Letters A, B, C, D, E are assigned to each unit length of periphery as shown in ...
17
votes
3answers
2k views

Fair results with unfair die

You are given a 6-sided die.The die is biased, so it is more likely to produce some results than others, but you don't know the exact odds. It is however given that the odds are the same for each roll,...
0
votes
1answer
7k views

10 little dwarves [duplicate]

A dwarf-killing giant lines up 10 dwarfs from shortest to tallest. Each dwarf can see all the shortest dwarfs in front of him, but cannot see the dwarfs behind himself. The giant randomly puts a ...
-6
votes
5answers
617 views

Password encryption

We are tasked with finding a password. Our only hint seems to be: Was wir wissen, ist ein Ozean; was wir nicht wissen, ist ein Tropfen. German for: What we know is an ocean, what we don't ...
5
votes
2answers
1k views

Markus' lucky numbers

It was late night when Markus was sitting at his desk and suddenly a fairy appeared out of nowhere. She told him that he had been granted a wish. Markus wished for her to tell him next week's lottery ...
5
votes
2answers
969 views

Theoretical Puzzle: Making a binary puzzle with a unique solution

If I have a table of binary values, and tell you the column and row counts for "on" or "1" values, is it possible to solve, with certainty, any grid of size n*m? Take the following puzzle for example:...
4
votes
2answers
2k views

Probability of three segments forming a triangle

Consider a line segment of length L. This segment is cut in three segments at arbitrary points. What is the probability that these three segments could be rearranged as sides of a triangle?
3
votes
1answer
354 views

Tower of tiles revisited

An S-tileset is a collection of n oriented tiles, where no two tiles have the same size, each tile is one unit thick, and its non-zero-integer length and width add up to n+1. (So, an S-tileset has n ...
7
votes
8answers
4k views

Divide 3 cakes into 4 equal parts?

You have three cakes of diameter 20cm, 16cm and 12cm respectively as shown in the figure. They all have the same height. Now your task is to divide these 3 cakes into 4 equal parts and you are ...
4
votes
2answers
13k views

Out of Glass Puzzle (MatchStick Puzzle)

The object is to move 2 matches to get the bluebottle to fly outside the glass. At the finish, the glass may be turned in any direction, but it must be exactly the same shape as before.
7
votes
5answers
2k views

How many squares can you find in the picture?

How many sqares can you draw in given pattern, when each corner of a sqare has to lie in the exact center of one of the 20 colored circles?
6
votes
3answers
1k views

Guess the last pattern in the image

Find the last pattern in the picture and state your reasons. source: zoomit.ir
51
votes
16answers
12k views

Join all circles together only with 6 lines

In the below image, can you draw 6 straight lines that pass all the circles? As soon as you start drawing lines you can't take your pen up until you draw all six lines. hint: you don't have to keep ...
5
votes
1answer
1k views

Put numbers from 1 to 6 in the puzzle

Put the numbers from 1 to 6 in the puzzle in a way such that: In each row or column there shouldn't are no duplicate numbers. The squares that are joined together have the same number.
1
vote
2answers
778 views

Who? What Color? Rank? Number? in a running match

There is a running match, but there isn't anyone to judge; we have only information that the audience gave us (but we know their info is true). We the have name, rank, T-shirt color, and T-shirt ...
6
votes
1answer
694 views

Unlocking a curiously-geared combination lock

The image shows numbers on ring-dials on a curiously-geared combination lock, where the current setting is (3,3,3,3) and ring sizes are (5,7,8,11), inner to outer. The setting (0,0,0,0) opens the ...
10
votes
3answers
5k views

Mirrored numbers

If you multiply $2178$ by $4$ you will get the same digits, but written in the back order, like if you look in a mirror: $2178 \cdot 4 = 8712$. How to find all possible natural numbers, that are ...
3
votes
2answers
848 views

How high a tower of tiles can be made?

An $S$-tileset is a collection of $n$ oriented tiles, where no two tiles have the same size, each tile is one unit thick, and its non-zero-integer length and width add up to $n+1$. (So, an $S$-...
6
votes
1answer
770 views

Cryptic Clue - “One who will succeed with melody, we hear” Answer - “Heir”

obviously I understand the definition part "One who will succeed". But can someone tell me how the word play part works in this clue? "with melody, we hear"
2
votes
1answer
338 views

Guess the Function for Scatterplot of Number Theoretic Function

To my knowledge, this puzzle is not previously published (except by me on google+ recently), but I would be interested to hear of any info otherwise. This following graph was generated using a simple ...
1
vote
2answers
389 views

Bottle rinsing with fixed amount of wash water

Given $L$ units of wash water, we want to wash out a vessel (eg, a milk bottle, honey jar, chemistry flask...) using a series of rinses that minimize the amount of Stuff other than water remaining in ...
2
votes
3answers
1k views

Folding a hexagon to a rectangle or square, with uniform overlap

A piece of fabric shaped like a regular hexagon with unit-length sides is given, with vertices A...F and center O. Let a fold correspond to folding some fabric along a straight line, without ...
18
votes
4answers
2k views

The 8-dimensional vegetable kebab

You are given two of each from the array of 8 vegetables numbered 1 to 8 as shown above. So in total you have 16 veggies(8 pairs). Your task is to make the longest kebab (sequence of vegetables ...
5
votes
5answers
3k views

A Set of Water Jug Challenges

You've probably heard about challenges with water jugs, so why not try a few? Use 3- and 5- liter jugs to get 4 liters. Use 5- and 7- liter jugs to get 4 liters. This one's different. How many ...
5
votes
3answers
2k views

A Sand Timer Challenge

Which (if any) of these intervals is it possible to measure given two sand timers (which change from question to question)? There are no minute marks, halfway points, etc. A. 7 minutes with 4- and 5-...
9
votes
2answers
431 views

A Martin Gardner problem about constructing a scoreboard given minimal information

The following is a paraphrasing of a problem from Martin Gardner called "Tricky Track." Three schools $-$ $A,B,C$ $-$ participated in a track meet with several events. Each school was awarded some ...
6
votes
1answer
497 views

Arranging cards in rows

This question appeared in an old math contest, and I seem to remember that the answer I had back when I first saw it was unsatisfactory. You have a deck of cards numbered from $1$ to $60$. First, ...
4
votes
1answer
499 views

What do the Glyphs from the Tale of Genji represent?

The Tale of Genji is a classic japanese novel, probably written more than a thousand years ago. The 19th century artist Toyohara Kunichika painted a picture for every of the 54 chapters. Every ...
7
votes
1answer
1k views

What is the “linguistically hardest” number less than $10^9$?

The linguistic hardness ($LH$) of a natural number is the ratio of the amount of letters in the writing of this number in English to the amount of its digits. For example, $LH(1234) = 7.75$, as: $$...
3
votes
2answers
496 views

Your age and my age [closed]

This is not a very difficult problem, but it seems that it hasn't been asked here. It's one of my favorites, so here we go: I am twice as old as you were when I was as old as you are. When you ...
11
votes
2answers
698 views

First number, which can not be defined

What is the appropriate answer to this question? What is the first natural number, which can not be defined with less than 15 words? Explanations: 1. Natural means integers greater than 0. ...
27
votes
5answers
4k views

First odd number in a “number dictionary”

All numbers between 1 and 1010 are written out and ordered alphabetically into a dictionary (as the only entries). Spaces and hyphens are removed. 1024 would then be "onethousandtwentyfour". Also, "...
6
votes
3answers
505 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 ...
10
votes
6answers
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!...
21
votes
12answers
125k 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....
9
votes
1answer
321 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 ...
20
votes
2answers
9k 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 ...
48
votes
11answers
259k views

6, the magic number

Here's a fun (albeit difficult) one: Make these equations true using arithmetic operations: ...
8
votes
1answer
546 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.
0
votes
3answers
42k 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.

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