40 votes
Accepted

Winning chance in coins game with fixing

GoblinGuide's user avatar
21 votes
Accepted

Two prisoners and twenty marbles

Same number of nights as in PDT's solution but perhaps expressed in a simpler way.
Florian F's user avatar
  • 29.8k
18 votes
Accepted

Make the three products equal and as large as possible

First observe that So we get this far: In order to maximize the product, So the answer is
Bubbler's user avatar
  • 14.1k
17 votes
Accepted

Tile a square as small as possible using two different sizes of square tiles

The answer is obviously Now consider But Therefore,
Bubbler's user avatar
  • 14.1k
15 votes
Accepted

75 integers are squared or cubed: minimum distinct results?

The minimum quantity of different results is This is because To concretely achieve this minimum, we can
isaacg's user avatar
  • 6,944
15 votes
Accepted

Make a square table top with the minimal needed amount of straight cuts

It can be done in (but not without 30 characters)
loopy walt's user avatar
  • 21.4k
14 votes
Accepted

Circles crossing every cell of an 8x8 grid

Here is my first try. I wonder whether one can do better. (actually it is not true. My first shot was 16 small circles...)
Florian F's user avatar
  • 29.8k
12 votes

Make a square table top with the minimal needed amount of straight cuts

Here is an answer with only straight cuts. See image below:
Lezzup's user avatar
  • 5,096
11 votes

Two prisoners and twenty marbles

They can do it in 10 nights at least:
PDT's user avatar
  • 12.3k
10 votes

Circles crossing every cell of an 8x8 grid

Bonus version: (I claim without proof that this is optimal)
Sunny Lu's user avatar
  • 2,864
10 votes

Flip counters in a grid so that they alternate in color

I am not sure if this is optimum but I can do it in six moves:
PDT's user avatar
  • 12.3k
10 votes

Make a square table top with the minimal needed amount of straight cuts

Another answer matching the current best number of cuts, but using only horizontal and vertical cuts (my brain doesn't work well with triangles).
calvenable's user avatar
8 votes
Accepted

Flip counters in a grid so that they alternate in color

A simple proof that PDT's solution is optimal:
Bubbler's user avatar
  • 14.1k
7 votes

Two prisoners and twenty marbles

Minimising worst case waiting time, one can not do better than the number of nights presented by others. One can not safely lower by one night, since the person going second then only has So with the ...
SE - stop firing the good guys's user avatar
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 ...
Will Octagon Gibson's user avatar
6 votes

Flip counters in a grid so that they alternate in color

Label the rows by A, B, C, D from top to bottom, and columns by 1, 2, 3, 4 from left to right. This is minimal because Also,
mathmandan's user avatar
  • 1,053
6 votes

Circles crossing every cell of an NxN grid

I think I am still a fan of concentric circles. Modulo some adjustments for the corners. Here is a 20-grid covered with 14 circles.
Florian F's user avatar
  • 29.8k
6 votes
Accepted

Make a square table top with six (or fewer) pieces

For a start, here is a 6-piece solution. From there you can find some variations. Here is a less boring one.
Florian F's user avatar
  • 29.8k
6 votes

Winning chance in coins game with fixing

This is not nearly as elegant as GoblinGuide's simple answer: https://puzzling.stackexchange.com/a/126192/1777 The probability of winning is always: Strategy: For any given N coins, there is: This ...
LeppyR64's user avatar
  • 13.6k
5 votes
Accepted

Number operation problem - find minimum number of operations

I can do it in seven operations: Alternative path, with smaller final numbers: EDIT: A quick computer search revealed what I should have seen by hand:
AxiomaticSystem's user avatar
5 votes

Circles crossing every cell of an NxN grid

My best effort: 1, 1, 2, 2, 3, 3, 4, 5, 6, 6, 7, 11, 11, 13, 16, 17, 19, 20, 20, 22. The larger ones are definitely suboptimal.
user1502040's user avatar
5 votes

Circles crossing every cell of an NxN grid

UPDATE: I found some nice symmetric solutions: N = 12 N = 14 N = 18 I found some new solutions N = 12 N = 13 N = 14, love that circle that breaks symmetry N = 15 N = 16 N = 17 N = 18 N = 19, ...
Dmitry Kamenetsky's user avatar
4 votes

Circles crossing every cell of an NxN grid

Making a community wiki so that all the answers are kept in one place. Anyone can edit it. N Circles (Current Best Known Upper Bound) Credit 1 1 trivial 2 1 trivial 3 2 user1502040 4 2 ...
3 votes

How many Chess Pieces are needed to control every square on the board? No Piece Restriction

There are two additional asymmetric cost-28 solutions (up to symmetry, the solutions differ by a single pawn): Found using programmatic search, code on GitHub. I disallowed more than 2 bishops on the ...
DPenner1's user avatar
  • 219
3 votes

6 Water Glasses Upside Down

I've solved this for arbitrary values of $n$ and $N$ ($n \leq N$) where, $n$ = glasses to select per move $N$ = total number of glasses My method showed no solution is possible when $n$ is even and $...
Abhinav Anand's user avatar
3 votes

Make a square table top with six (or fewer) pieces

My (boring) 6 solution; and (cool) 7 piece solution for inspiration.
Retudin's user avatar
  • 8,683
3 votes

Circles crossing every cell of an NxN grid

Here are two solutions that yielded the best-known values (not necessarily optimal). $N=12$: $N=13$:
RobPratt's user avatar
  • 13.7k
2 votes

Flip counters in a grid so that they alternate in color

I think I found a 6 move solution different to PDT
Christian Vaughn's user avatar
2 votes

Connecting 3 circular power timers to lights so that they turn for one day on Christmas

Here is another solution. Sill 95 days and 23 3/4 hours before Christmas. But the lights remain completely off for the whole time until Christmas, then turn on for 24 hours and switch off again. How ...
Florian F's user avatar
  • 29.8k
2 votes

Make the three products equal and as large as possible

One derived rule limits the amount of choices for the 6 numbers and their positions
FirstName LastName's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible