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
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 ...
17
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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,...
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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
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2answers
947 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:...
7
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8answers
3k 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 ...
6
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1answer
693 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
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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 ...
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 ...
18
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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 ...
9
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2answers
429 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
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1answer
493 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, ...
7
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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
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2answers
495 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 ...
27
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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, "...
20
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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
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11answers
252k views

6, the magic number

Here's a fun (albeit difficult) one: Make these equations true using arithmetic operations: ...
8
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1answer
545 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.
5
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1answer
560 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'...
7
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2answers
745 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 ...
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5answers
2k 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 ...
8
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2answers
467 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 ...
4
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1answer
858 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 ...
2
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1answer
829 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 ...
19
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3answers
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. ...
14
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7answers
2k 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 ...
5
votes
1answer
606 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 ...
27
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3answers
4k 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 ...
0
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1answer
1k 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 ...
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5answers
903 views

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?
0
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2answers
565 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 \...
5
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1answer
124 views

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 $M$. ...
5
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2answers
1k views

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 $\...
114
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9answers
18k views

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 ...
16
votes
2answers
11k 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 ...
4
votes
6answers
4k 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 ...
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
votes
1answer
604 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
948 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
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3answers
976 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
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2answers
613 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 ...
81
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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
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1answer
730 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
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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
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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 ...