Questions tagged [mathematics]

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

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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 ...
Ali's user avatar
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20 votes
3 answers
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. ...
Per Manne's user avatar
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15 votes
7 answers
4k 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 ...
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5 votes
1 answer
723 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 ...
MrHen's user avatar
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34 votes
3 answers
7k views

Maximum time for ants to fall off stick

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 ...
justhalf's user avatar
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1 vote
1 answer
2k views

Minimum number of weights you need to define any integer weight from 1 to N

Following this question What's the fewest weights you need to balance any weight from 1 to 40 pounds? I am interested what is the minimum number M of weights you need to define any integer weight ...
klm123's user avatar
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1 vote
5 answers
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I Eight Two Much

If four 2s make eight, and three 2s also make eight, how many 2s do you need to make three eights, when you only have less than eight 2s?
Thassa's user avatar
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0 votes
2 answers
721 views

Number of ways to fold a 2x4 map

M.Gardner in his book "Mathematical puzzles and diversions" states that the following 2x4 map $$ \begin{array}{|c|c|} \hline 1 & \phantom{1} & \phantom{1} & \phantom{1} \\ \hline \...
klm123's user avatar
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6 votes
1 answer
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When can one construct expression dividable by M from any N numbers?

You have N numbers written in one row. One needs to put any amount of the four symbols $($, $)$, $+$, and $\times$ between them in such a way that the resulting expression is divisible by $M$. What ...
klm123's user avatar
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3 votes
1 answer
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Is there a more specific name for this type of arithmetic puzzle?

There are arithmetic puzzles with some numbers (typically four) and rules for combining them (perhaps just the four basic arithmetic operators or including things like combining digits 2 and 3 to make ...
ClickRick's user avatar
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7 votes
3 answers
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How many digits can be removed from a division puzzle?

Similarly to How many digits can be removed from a multiplication puzzle and still give only one answer? I am curious about division puzzles. I know this puzzle: . It has only 2 out of 42 digits $\...
klm123's user avatar
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127 votes
12 answers
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Paying the Troll toll

You are on your way to visit your Grandma, who lives at the end of the valley. It's her birthday, and you want to give her the cakes you've made. Between your house and her house, you have to cross 7 ...
Shevliaskovic's user avatar
25 votes
3 answers
19k views

Write twenty-four from four numbers

Write 24 using the four numbers 1, 3, 4, 6 and basic arithmetic. Explanations: The given are numbers, not digits, so you can't group them using decimal notation. For example, you can't create the ...
klm123's user avatar
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4 votes
6 answers
7k views

Writing numbers puzzle

How do you write 23 using only the number 2? 34 using only the number 3? 56 using only the number 5? 100 using only the number 9? You can use only the numbers said, but any math you want in order ...
Shevliaskovic's user avatar
3 votes
2 answers
653 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 ...
klm123's user avatar
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6 votes
1 answer
899 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 ...
arshajii's user avatar
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13 votes
7 answers
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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 ...
klm123's user avatar
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6 votes
1 answer
1k 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 in ...
Xynariz's user avatar
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29 votes
7 answers
9k 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 ...
WendiKidd's user avatar
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6 votes
3 answers
1k 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): ...
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10 votes
2 answers
740 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 ...
Fengyang Wang's user avatar
96 votes
7 answers
25k 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 ...
WendiKidd's user avatar
  • 2,423
13 votes
1 answer
1k 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 ...
mau's user avatar
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24 votes
3 answers
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 < 1/2, he with ...
arshajii's user avatar
  • 2,188
23 votes
4 answers
8k 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 ...
kaine's user avatar
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21 votes
3 answers
7k 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 ...
kaine's user avatar
  • 9,102
16 votes
1 answer
4k 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 ...
PM.'s user avatar
  • 265
16 votes
4 answers
6k views

The Mexican Standoff

There are three cowboys in a Mexican standoff against each other, named Juan, José, and Jorge. Juan is the straightest shooter in the West, and can hit his target 100% of the time. José, who has a ...
user avatar
13 votes
4 answers
13k 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 ...
user avatar
5 votes
1 answer
818 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 ...
awesomepi's user avatar
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49 votes
4 answers
16k views

I don't know the two numbers... but now I do

Two perfect logicians, Summer and Proctor, are told that integers 𝑥 and 𝑦 have been chosen such that 1 < 𝑥 < 𝑦 and 𝑥 + 𝑦 < 100. Summer is given the value 𝑥 + 𝑦 and Proctor is given ...
durron597's user avatar
  • 2,374
85 votes
16 answers
208k 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 ...
user avatar
13 votes
2 answers
2k 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?
John Bupit's user avatar
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39 votes
3 answers
6k 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 ...
Ross Millikan's user avatar
9 votes
3 answers
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 ...
diabonas's user avatar
  • 968
5 votes
4 answers
2k 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 ...
Ross Millikan's user avatar
24 votes
5 answers
7k 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. ...
Gilles 'SO- stop being evil''s user avatar
122 votes
7 answers
30k 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; each may ...
Jaydles's user avatar
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