All Questions
Tagged with construction mathematics
27
questions
11
votes
9
answers
3k
views
Can you arrange 25 whole numbers (not necessarily all different) so that the sum of any three successive terms is even but the sum of all 25 is odd?
To allow new users to solve this puzzle and earn reputation points, I encourage all users whose reputation is 200 or more to not post an answer until 48 hours after this question is posted. Thank you!
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- 12.5k
21
votes
5
answers
3k
views
Mishustin's circle problem
This problem was given to high school students by the Russian prime minister Mishustin.
We have a circle. We are given some point on the circle and its diameter, as shown below. We are given a ...
- 36.3k
9
votes
2
answers
431
views
Colour the positive integers without making a blue equation
This puzzle is related to How do we find the numbers? but has a slightly more striking solution in my opinion. It is also based on one of my MathsSE answers.
What is the least number of colours you ...
- 7,820
7
votes
0
answers
197
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Can you construct a nonagon with 47 rods?
Stiv's Diabolical Instruments now offers a bundle of exactly 47 equal-length rods that can be joined by hinges at their ends – and only the ends – to form planar linkages (i.e. all hinge axes are ...
- 7,820
23
votes
3
answers
2k
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A pentagon that can measure the first 7 integer distances
A pentagon can be used to measure 10 distances - one distance between each pair of its 5 vertices. Can you find a pentagon that can measure every integer distance from 1 to 7, inclusive?
- 36.3k
14
votes
4
answers
2k
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The Game of Golden Squares
On a magic chessboard of infinite size, the squares are either wooden or golden. If 4 or more of its 8 neighbors (a king's move away) are golden, a wooden square becomes golden the next day. Golden ...
- 6,536
10
votes
2
answers
578
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Permutations of first 10 natural numbers such that all the prefix sums are distinct
I posted this question on Math SE as well. Did not receive any help.
This is a question that I was asked in a Quant Interview. I would like you all to have a crack at this. I could not find a problem ...
- 201
11
votes
2
answers
254
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Rigid regular nonagon from 21 Meccano strips
You are given 21 Meccano strips, where the distance between adjacent holes is 1 unit:
9 strips of length 10 (hence having 11 holes)
6 strips of length 18 (19 holes)
6 strips of length 19 (20 holes)
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- 7,820
8
votes
0
answers
277
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Doubling the cube with rational Meccano strips
In three monographs published in 2006, 2008 and 2014 Gerard 't Hooft considered "Meccano mathematics": how to construct specified distances and regular polygons by a rigid system of ideal ...
- 7,820
10
votes
2
answers
393
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Gentrification in Chessshire
You can skip the back story and directly jump to the question.
Capitalism has arrived in suburban Chesster the community most famed for The Game, and with a vengeance. Rents have trebled in less than ...
- 21.3k
1
vote
1
answer
123
views
Self-indulgent numbers
Let's call a positive integer N self-indulgent of degree K>2 if for every positive integer k<K the following is true:
More than half of the first k multiples N,2N,...,kN of N contain with ...
- 21.3k
4
votes
1
answer
238
views
Infinite beauty
This is a follow-up to Puzzle about 6 infinite cylinders in space
Question:
Given six identical infinite (no caps) cylinders is there a beautiful arrangement in space such that each touches each ...
- 21.3k
3
votes
1
answer
203
views
Universal bisectors
A bisector is something that cuts some other thing into two equal pieces. More concretely, assume we are given a reasonably well-behaved (for example, compact) 3D object and we are looking for planes ...
- 6,205
0
votes
1
answer
127
views
A rectangle with non-integer side lengths [duplicate]
Is it possible to build a gapless rectangle with non-integer side lengths using rectangles each with two integer side length and two non-integer side length?
The rectangles are not required to be the ...
- 12.2k
6
votes
1
answer
320
views
Triangles, rectangles, nonagons
Which is the nonagon with the least area and which fulfills the following conditions.
The nonagon has to be made from 7 triangles and 3 rectangles, all having side-lengths that are integer numbers.
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- 2,915