Questions tagged [mathematics]

A puzzle strongly related to mathematical facts and objects, or whose solution needs serious mathematical arguments. General mathematics questions are off-topic but can be asked on Mathematics Stack Exchange.

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3
votes
2answers
615 views

Does this strategy work?

I'm thinking about the following strategy for Fastest way to collect an arbitrary army: When a soldier decides to go to some house he "reserves" it. Once a soldier is free (has delivered the news to ...
6
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1answer
607 views

What is the expected length of the longest piece?

If a rod of unit length is broken into $n$ pieces, what is the expected length of the longest piece? The positions at which the rod is broken are chosen randomly uniformly. This is a generalization ...
12
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7answers
3k views

Fastest way to collect an arbitrary army

I am looking for solution of this puzzle: There is a kingdom with a square shape with sides of length 1. The castle is located at the center of the square. At the castle the king lives under the ...
4
votes
1answer
951 views

Odds of duplicate birthdays

I found the following problem in an number of places online: John once bet a fellow gambler that two of the first thirty persons they met and spoke to would prove to have the same birthday. Strong ...
29
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7answers
8k views

Aside from brute force, how can I solve this puzzle?

Once upon a time, and old lady went to sell her vast quantity of eggs at the local market. When asked how many she had, she replied: Son, I can't count past 100 but I know that: If you ...
5
votes
3answers
978 views

How many digits can be removed from a multiplication puzzle and still give only one answer?

There's a common category of mathematical puzzle which involves determining missing numbers in a long multiplication problem. As an example from this site (problem 10): ...
9
votes
2answers
615 views

What size of puzzle is appropriate?

I am making a puzzle based on a Project Euler problem. Here is the puzzle at present: What path in the triangle below, starting from the top number with each step moving to one adjacent number in ...
82
votes
7answers
17k views

Why does this solution guarantee that the prince knocks on the right door to find the princess?

I found this puzzle online: On the top floor of a castle lives a princess. The floor has 17 bedrooms arranged in a row. Each bedroom has doors connecting to the adjoining bedrooms as well as to the ...
13
votes
1answer
743 views

A building with an odd elevator

In a building, there is an odd elevator, which has only two buttons: UP, which makes it go up 9 floors, and DOWN, which makes it go down 7 floors. (The ground floor is floor 0.) It is possible to ...
21
votes
3answers
3k views

Winning an unfair game

I came across the following interesting problem today: A game consists of a sequence of plays; on each play either you or your opponent scores a point, you with probability $p < \frac{1}{2}$, he ...
23
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4answers
6k views

Variation of 100 prisoners light problem

There is a classic problem below for which Dr. Yisong Song wrote a very well written and thought out series of solutions. The variation here I've never seen anywhere but am curious. I want to work it ...
17
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2answers
3k views

N pirates steal their share of bananas to the benefit of a monkey

The following is a type of logic / math puzzle I've yet to see on this site. I feel it belongs because the kernel of this problem can be reworked into other puzzles. $N$ pirates find themselves ...
14
votes
1answer
3k views

How do you solve the circular table problem?

One classic puzzle has many different forms, but the basic strategy is the same. Once upon a time there was a crazy king who had a very wise minister with him. The king had a habit of playing a ...
10
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4answers
8k 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 ...
5
votes
1answer
725 views

Shuffling Cards

I was just thinking about this. Let's say that we have a card deck with 54 cards and the $n$th card from the top is flipped. We repeat a short process of cutting the deck directly in the middle and ...
57
votes
10answers
43k views

A camel transporting bananas

A somewhat well-known puzzle is described as such: You have a pile of 3,000 bananas. You wish to transport them to a place 1,000 miles away on the back of a camel; however, the camel can only carry ...
13
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2answers
1k views

End of the world - on a Sunday?

If the end of the world was supposed to come on the first day of a new century, what would be the chances that it would happen on a Sunday?
33
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3answers
5k views

Pirates and gold coins

A group of N pirates has come by a chest containing 200 gold coins. Their rules require that the coins be distributed by the following approach. The pirates are ranked from fiercest to meekest and ...
9
votes
3answers
2k views

Sliding Bolt Puzzle - fastest solution (time-wise)

This is a follow-up question for the Sliding Bolt Puzzle. If you have not solved it yet, you might want to head there first, as the extended discussion of its solution in this question will contain ...
5
votes
4answers
1k views

Round-Robin Tournament

20 teams played in a round-robin tournament. The winner of each game got 1 point, and the loser got 0; there were no draws. Each team's total score was a square number. At least one team had a unique ...
14
votes
5answers
5k views

N logicians wearing hats of N colors

N logicians are wearing hats which can be of N different colors (each hat has one color; there can be multiple hats with the same color). Each logician can see the colors of all hats except his own. ...
109
votes
6answers
24k views

100 Prisoners' Names in Boxes

Names in Boxes The names of 100 prisoners are placed in 100 wooden boxes, one name to a box, and the boxes are lined up on a table in a room. One by one, the prisoners are led into the room;...