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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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 ...
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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 ...
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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 ...
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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 ...
user88
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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:
$$...
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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 ...
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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, "...
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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 ...
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6, the magic number
Here's a fun (albeit difficult) one:
Make these equations true using arithmetic operations:
...
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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.
user360
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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'...
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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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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 ...
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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 ...
user88
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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 ...
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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 ...
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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.
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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 ...
user88
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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 ...
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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 ...
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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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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?
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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
\...
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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 ...
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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 ...
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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 $\...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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):
...
user20
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
user88
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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 ...
user88
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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 ...
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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 ...
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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 ...
user88
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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?
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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 ...
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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 ...
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