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 do you get 5 by using the numbers 2, 2, 3 and 5?
You can use addition, multiplication, subtraction, and division as many times as you want but can only use the numbers one time each.
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Three-cushion billiards challenge.
World champion three-cushion billiards player can perfectly make a billiard ball end where asked for (if possible), on a standard rectangular shaped competition table.
The champion now, for ...
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Sliding coins down an envelope
The envelope is a regular pentagon with two diagonals. The red coins are two vertically aligned and touching congruent circles, the top one passing through the apex of the pentagon, and the bottom ...
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How many gloves do we need to randomly select to ensure each octopus will have 8 different colored gloves? [closed]
The restaurant is a major sponsor of the Aquatic Boxers’ Club. From time to time, two octopuses from the ABC are invited to the restaurant to put on a boxing match in an aquarium, for the ...
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Multiplying pounds and shillings swaps the numbers
If you double £6 13s, you get £13 6s, which is merely changing the shillings and the pounds.
Can you find all the other sums of money that has the same peculiarity that, when multiplied by any integer ...
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Is there a Python solver for the Picture-Cube?
I'm working on a CayleyPy project where we study the diameters of graphs that come from different combinatorial puzzles. At the moment I’m focusing on the Picture-Cube, a 3×3×3 puzzle where each move ...
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The sum of divisors of current year is also the current year
We already knew that the current year is sum of first 9 perfect cubes and there is another hidden interesting fact.
But there is another twist: The sum of divisors of current year is also the current ...
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Heptagons trompe-l'œil ?
Seven outer blue, equal sized, regular heptagons touch the sides of a given, also equal sized, inner blue regular heptagon.
The green triangle has black vertices: the south and the, up to one, most ...
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What pattern did Excel see in my data?
I was filling out the rightmost column of this set of cells from top to bottom. (The content of that column is intended to be manually calculated using the numbers to the left plus some hidden weights,...
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When is the next Narcissistic date?
A Narcissistic date is a date such that when all digits of a date is raised to certain nth power and add them all together, the sum is equal to YYYY.
As an example, if we take today's date, which is ...
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Sum of a sequence
The last two days I have dreamt of solving a puzzle to escape hospital, and I just woke up so wanted to jot this down quick.
Imagine a snake with some number of segments. The segments' labels are $(1,\...
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Can another circle fit in this diagram?
Two vertically-aligned and touching congruent (blue) circles are inscribed in a pendant (the black quadrilateral) in a regular star as shown below. Can you fit another circle of the same size that’s ...
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When is the next "Factorion" date?
A "Factorion" date is a date such that when written to either one of M!+M!+D!+D!+Y!+Y!+Y!+Y! (MM/DD/YYYY), D!+D!+M!+M!+Y!+Y!+Y!+Y! (DD/MM/YYYY) , or Y!+Y!+Y!+Y!+M!+M!+D!+D! (YYYY/MM/DD) is ...
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Two semicircles in a regular pentagon
Two semicircles, pink and blue, are inscribed inside a regular pentagon as shown in the figure. Which semicircle is bigger?
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a 1:1:1 mixing?
Four colors puzzle:
You have three colors. You can change their opacity and overlay them, or reuse them. Your goal is to obtain a 1:1:1 mixing (i.e., one third green, one third blue, one third yellow),...
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Is 1,111,111,111,111 prime? Not even close!
Inspired by this question, I pose one that leans in the opposite direction.
The number 1,111,111,111,111 is not only composite. It has a factor quite small compared with what one might expect for a ...
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Show that the area of the region inside this square and regular pentagon is greater than 3/4
A square and a regular pentagon, each of area 1, are coplanar and concentric. Show that the area of the region inside both shapes is greater than 3/4.
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Is 1,111,111,111,111,111,111 prime?
Now I am rereading the good old book "The Canterbury puzzles and other curious problems" by Henry Ernest Dudeney. In the introduction he presents the following illustration of puzzle ...
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Is there a perfect squared square made entirely of squares of prime edge?
There are infinitely many sets of distinct primes whose squares add up to a square number and, presumably, sets of any size (https://mathoverflow.net/questions/501745/primes-whose-squares-add-up-to-...
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Show that the triangle has a 60° angle
On square ABCD, points E and F lie on sides BC and CD, respectively, such that BE=CF.
Line BD intersects lines AE and AF at G and H, respectively.
Using pure geometry, prove that a triangle with side ...
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Angle between lines on pentagons
The two regular pentagons share a vertex and an edge. What’s the angle between the red and blue lines?
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Which triangle has the larger area?
In the diagram, AFH, ABGF, ABCDE are all regular polygons.
Which triangle has larger area: red or blue? Or do they have the same area?
Note: Geogebra can be used to help, but an answer saying "...
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The "e" in apple
I cut a thin slice from a spherical apple, cutting along a plane.
Then I realized, there is an "e" in apple.
Why is there an "e" in apple?
Hint:
EDIT: Puzzling Meta post about ...
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My Six Children
The sum of the ages of my three boys, who are all different ages, is equal to the product of my three daughters' ages; vice versa, the sum of my three daughters' ages is equal to the product of my ...
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yet another machine giving O or X for sequences of positive numbers
The excellent recent puzzle
What is the pattern of this mystery box?
immediately made me consider a solution which turned out to be very much unrelated and hence obviously wrong.
Here is another ...
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