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Results tagged with optimization
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user 80061
A puzzle where you have to optimize a certain objective function (maximize profit, minimize cost). There should ideally be a provable best answer, to avoid making the puzzle into an [open-ended] game.
9
votes
1
answer
485
views
Tile a square as small as possible using two different sizes of square tiles
There are two types of square tiles. One type has a side length of 1 cm and the other has a side length of 2 cm.
What is the smallest square that can be made with equal numbers of each type of tile?
…
- 21.3k
6
votes
Make the three products equal and as large as possible
This is intended only as a partial answer:
Bubbler’s answer gave an arrangement of the six numbers where the product of the numbers (for each edge) is:
The following is a proof that the common produc …
- 21.3k
23
votes
7
answers
3k
views
You are at a crossroads with five roads leading away from it
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! …
- 21.3k
6
votes
4
answers
920
views
Flip counters in a grid so that they alternate in color
Beginner puzzle
This puzzle is intended to be suitable for people who are new to puzzle solving.
Clarification: Both experienced solvers and new solvers are welcome to post solutions to this puzzle.
…
- 21.3k
23
votes
1
answer
3k
views
What’s the highest salary the greedy king can arrange for himself?
A little kingdom contains 66 people, a king and 65 citizens. Each of them, including the king, has a salary of one gold piece. When democracy comes, the king is denied a vote, but he has the power to …
- 21.3k
0
votes
1
answer
131
views
What is the smallest number of glasses the team can move to perform Coach Newton’s challenge?
Beginner puzzle (suitable for people who are new to puzzle solving)
Coach Newton sets up ten glasses arranged in a triangle as shown, with the glasses numbered 2, 3, 7, 8, 9, and 10 full of water and …
- 21.3k
15
votes
4
answers
3k
views
What is the smallest interval between two palindromic times on a 24-hour digital clock?
A 24-hour digital clock occasionally shows times that are palindromes such as 0:34:30, 21:33:12, and 1:20:21, if we ignore the colons.
What is the smallest interval between two such times?
Clarificati …
- 21.3k
15
votes
3
answers
993
views
What is the greatest possible number of empty squares that could remain after the jumps? [duplicate]
There is a kangaroo in the centre of each square of a 5x5 grid of squares. Lightning strikes, and each kangaroo simultaneously jumps one square up, down, left or right to an adjacent square in the gri …
- 21.3k
7
votes
What is the greatest possible number of empty squares that could remain after the jumps?
Partial answer only:
The idea for this partial answer came from Rob Pratt’s answer.
If the kangaroos jump like this:
then after the jumps, the kangaroos will occupy 16 blue squares:
and the 16 blue …
- 21.3k
15
votes
1
answer
686
views
Minimize the number of pieces in the cube that you build
Consider the following slanted pyramid which is made from 30 unit cubes:
Step 1: Delete any 3 unit cubes. There is no restriction on which unit cubes are deleted. These 3 deleted unit cubes are no …
- 21.3k
18
votes
4
answers
1k
views
Make the three products equal and as large as possible
Beginner puzzle
This puzzle is intended to be suitable for people who are new to puzzle solving.
Clarification: Both experienced solvers and new solvers are welcome to post solutions to this puzzle.
…
- 21.3k
11
votes
2
answers
2k
views
How quickly can Zeus get to his destination?
Zeus starts at the origin (0,0) and can make repeated moves of one unit either up, down, left or right, but cannot make a move in the same direction twice in a row.
For example, he cannot move from (0 …
- 21.3k
5
votes
1
answer
980
views
Anna and Boris play the Red Blue game
Anna and Boris play a game on a 9x9 chessboard. Anna goes first and turns alternate thereafter. In each move, Anna puts a red counter on a vacant square while Boris puts a blue counter on a vacant squ …
- 21.3k
6
votes
16
votes
3
answers
4k
views
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 mat …
- 21.3k