Questions tagged [construction]
A puzzle that requires an example to be built that fits certain criteria.
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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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Can you color the 8x8 grid red and blue?
Consider an 8x8 grid made up of 64 unit squares. The goal is to color the 64 squares red or blue so that the following two constraints are satisfied:
ROWS: For every pair of adjacent rows, exactly ...
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Make exactly 101 squares using as few lines as possible
With how few straight lines can you make exactly 101 squares? The squares don’t necessarily have be the same size.
Clarification 1: By lines, I mean you can use mathematical line segments and/or ...
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Are circles required on the edge of the grid? Part 2
This question is a follow up to a previous question:
Are circles required on the edge of the grid?
The image below is a puzzle from the FlowFree app.
Notice there are no colored circles on the edge of ...
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Are circles required on the edge of the grid?
The image below is a puzzle from the FlowFree app:
The image below is my solution to the above puzzle:
The rules stated in the app are:
Drag to connect matching colors with pipe, creating a flow.
...
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The ultimate backgammon
The following position, where one player has borne off all their checkers while all of the other player's checkers are on the bar (thus losing a backgammon), is reachable by a legal sequence of dice ...
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Binary Grid Challenge and X & O Conundrum
You are given a 5x5 grid with some cells filled with either "X" or "O". Your goal is to fill the remaining cells with "X" or "O" following these rules:
Each row ...
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Pawns and a chessboard with no three aligned
This little problem crossed my mind and appeared to be not quite trivial.
How can you place P pawns on a chessboard with the constraint that no pawn is exactly midway between two other pawns?
Sure ...
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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 ...
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A balanced banquet
As your king's fitness adviser you have been tasked with optimising His Majesty's diet. This entails making sure that the king eats equal amounts of carbs (rooks), fat (bishops) and protein (knights). ...
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What's the most distant chess position?
It's well known that the combinatorial explosion means that there are many, many, possible chess games. And yet most games are decided within 100 moves, and Wikipedia says that the longest tournament ...
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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 ...
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A position where both sides have no moves at all, not even to put yourself in check
Inspired by this: No moves at all, not even to put yourself in check
Similar to the question linked above, find an arrangement using the fewest chess pieces (total from both sides), except for this ...
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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 ...
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- Pandora's Box -
After Prometheus had stolen fire from heaven and bestowed it upon mortals, Zeus, the king of the gods, determined to counteract this blessing. Zeus commissioned Hephaestus, the god of fire, to fashion ...
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Logical Deduction Persistence Test
In the grid below, create a path that starts at cell 1 and ends at cell 49, moving horizontally and vertically only.
The path must touch each of the 49 cells exactly once and contain a:
A. Maximum of ...
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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?
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Efficient Mowing at PSE
Your task:
Find the most efficient mowing path around the dark green bushes that mows (passes over) all of the grass (light green).
For those who cannot view the image above, there are 9 rows of 16, ...
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Symmetrical Chess Position With No Legal Moves
Your task is to set up a symmetrical (both vertically and horizontally) position on the first 7 ranks of a chess board that meet all of the criteria below.
For this puzzle, there is no eighth rank. It ...
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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 ...
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4x4 word grid optimization
Given that each letter in the English alphabet has a position:
$$a = 1, b = 2, ..., z = 26$$
Can you place 16 different letters such that:
Each row, column and diagonal forms a 4-letter valid English ...
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A Tetris puzzle made with love
I love designing perfect clear puzzles for my dear friend who loves Tetris. Here's a lovely puzzle I crafted today.
Original Puzzle (Warm-Up)
Starting with this field,
place this exact sequence of ...
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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 ...
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Quickest mate with Queens exchange
If both players cooperate, what is the quickest mate in chess that includes a Queens exchange, in a legal game?
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Smallest number of moves to reach a "reverse checkers" position
A "reverse checkers" position is a position where every piece for one player is on one colour and every piece for the other player is on the other colour. Consider this position, for example:...
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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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Make a topological torus-with-a-hole out of congruent squares that may share an edge or a vertex with other squares
Suppose we arrange, in 3-dimensional space, 8 identical solid cubes in space so they form a square-shaped ring (using a 3x3 arrangement of squares except for the one in the middle).
Its surface will ...
user76726
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Clash of the Robinsons
"Ridiculous!" you think "What can be the odds? Either I'm hallucinating or the amateur writing this story plunged to new depths of incompetence." Both being equally likely you don'...
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Longest chain of checks and captures
On a standard size chessboard, with white to move, make a configuration of chess pieces and moves, so that with every move by white the black king repeatedly becomes checked. With every move black ...
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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 ...
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