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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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6 votes
2 answers
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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 ...
ThreeFx's user avatar
  • 2,466
5 votes
2 answers
1k 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:...
KevinOrr's user avatar
  • 153
7 votes
8 answers
7k 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 ...
Hubble07's user avatar
  • 1,313
6 votes
1 answer
761 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 ...
James Waldby - jwpat7's user avatar
10 votes
3 answers
6k 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 ...
klm123's user avatar
  • 16.3k
2 votes
1 answer
386 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 ...
vzn's user avatar
  • 131
1 vote
2 answers
422 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 ...
James Waldby - jwpat7's user avatar
23 votes
4 answers
3k 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 ...
Hubble07's user avatar
  • 1,313
9 votes
2 answers
457 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 ...
ant11's user avatar
  • 638
9 votes
2 answers
943 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, you ...
user avatar
7 votes
1 answer
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: $$...
klm123's user avatar
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3 votes
2 answers
518 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 ...
bonob's user avatar
  • 133
29 votes
5 answers
5k 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, "...
355durch113's user avatar
23 votes
2 answers
13k 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 ...
ThreeFx's user avatar
  • 2,466
49 votes
11 answers
288k views

6, the magic number

Here's a fun (albeit difficult) one: Make these equations true using arithmetic operations: ...
ThreeFx's user avatar
  • 2,466
7 votes
2 answers
648 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.
user avatar
8 votes
1 answer
629 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'...
klm123's user avatar
  • 16.3k
7 votes
2 answers
794 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 ...
Calvin's Hobbies's user avatar
14 votes
5 answers
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 ...
klm123's user avatar
  • 16.3k
9 votes
2 answers
537 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 ...
user avatar
3 votes
1 answer
1k 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 ...
klm123's user avatar
  • 16.3k
2 votes
1 answer
889 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 ...
Ali's user avatar
  • 698
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
  • 961
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 ...
user avatar
5 votes
1 answer
728 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
  • 261
35 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
  • 6,043
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
  • 16.3k
1 vote
5 answers
938 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?
Thassa's user avatar
  • 147
0 votes
2 answers
726 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
  • 16.3k
6 votes
1 answer
145 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 $M$. What ...
klm123's user avatar
  • 16.3k
3 votes
1 answer
434 views

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
  • 1,823
7 votes
3 answers
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 $\...
klm123's user avatar
  • 16.3k
127 votes
12 answers
30k 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 ...
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
  • 16.3k
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
  • 16.3k
6 votes
1 answer
907 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
  • 2,188
13 votes
7 answers
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 ...
klm123's user avatar
  • 16.3k
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
  • 3,620
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
  • 2,483
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): ...
user avatar
10 votes
2 answers
742 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
102 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
  • 2,483
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
  • 2,095
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
  • 9,122
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
  • 9,122
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
14 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