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29 votes
Accepted

One rectangle, indivisible

The best you can do is one with an area of 30 (5 x 6): Disproving smaller cases 2 x 2 and 2 x 3 2 x anything 3 x 3 3 x 4 3 x anything 4 x 4 4 x 5 4 x 6 5 x 5 So that's definitely not an ...
Dan Russell's user avatar
24 votes

One rectangle, indivisible

Here is a proof that 5x6 is the smallest possible rectangle. A rectangle of size $x$ by $y$ has $\frac{xy}{2}$ dominoes and $x+y-2$ potential lines. All of these lines must be blocked by at least one ...
f'''s user avatar
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20 votes

Dominoroto-toto

First, let us define some things: For simplicity, for partial boards presented (with ...), let's consider that the width is equals to or larger than the height. If ...
Victor Stafusa - BozoNaCadeia's user avatar
14 votes
Accepted

The five problems of the six domino tiles

Problem 1: Problem 2: Problem 3: Problem 4: Problem 5:
Glorfindel's user avatar
  • 28.1k
13 votes

One rectangle, indivisible

I'll one-up you guys and prove this stronger statement: If $m\geq n$ are the dimensions of a rectangle that admits a nonsplittable domino tiling using more than one domino, then $m \geq 6$ and $n \geq ...
Anon's user avatar
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13 votes
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Tiling a chessboard

The answer is because
Deusovi's user avatar
  • 147k
11 votes

Introducing Domidoku!

Final Solution(Though its already answered, I wanted to solve it on my own as a part of learning. Due to an ongoing problem with imgur, it took too long for uploading the solution) SUDOKU Solution. ...
Techidiot's user avatar
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11 votes
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A puzzle with dominoes

There was one idea I had that made constructing a solution a lot easier. Here is the solution I came up with.
Jaap Scherphuis's user avatar
10 votes

How many tilings by dominoes of this region?

I count: reasoning:
thugsinuggs's user avatar
10 votes
Accepted

Piece de Resistance - Two Boxes, Two Boxes of Letters

With a friendly nod to @jafe (who came very close), since an hour has gone by I figured it was fair game to post my own independent solution… Didn't want to be seen as sniping or piggy-backing! This ...
Stiv's user avatar
  • 144k
9 votes

The First Lady's Dominos

Partial answer The first clue indicates Using this, we can convert the dominoes to
Zandar's user avatar
  • 3,592
9 votes

What is the largest domino ring that can be made?

In a ring, The given dominoes have three 1s, three 2s, four 3s, three 4s, five 5s. So 1, 2, 4 and 5 occur an odd number of times.
Jaap Scherphuis's user avatar
9 votes
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Domino tiling on 8x8 checkerboard with four squares removed

Here is my attempt at a proof. First I'll prove a useful set of shapes that can be covered by dominoes when two opposite-coloured squares are removed. Now let's apply this to the problem at hand.
Jaap Scherphuis's user avatar
9 votes
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Progressive matrix of dominoes

It looks like it should be because
SQLnoob's user avatar
  • 8,570
8 votes
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Cover the terrace with "slashed" tiles

It is as demonstrated by this image:
Zerris's user avatar
  • 4,681
8 votes
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Introducing Domidoku!

I worked with @Techidiot's sudoku solution and solved the Dominosa: The key to understand is that unlike regular Dominosa there are no tiles with same digits. and the grey cells indicate cells that ...
Ivo's user avatar
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8 votes
Accepted

Wednesday's Unmatched Donimoes Problem

edderiofer's user avatar
  • 2,371
8 votes
Accepted

Friday's Dominosa Problem

Here is the solution: Explanation (red): Continued (orange): Continued (yellow): Finally (green): Thanks for making these puzzles and enjoy your well-deserved weekend!
Glorfindel's user avatar
  • 28.1k
7 votes

A puzzle with dominoes

Here's another solution. I also used Jaap's clever restriction; it's much easier to verify the solution by hand after using that particular limitation. This solution has twelves in the inside corners ...
Bass's user avatar
  • 77.6k
7 votes
Accepted

How many tilings by dominoes of this region?

the answer is There are mendatory dominoes with the line :
Fabich's user avatar
  • 7,165
7 votes
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The First Lady's Dominos

So I think it's Some reasoning.
Matt's user avatar
  • 10.9k
7 votes
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4 walls of domino tower

As noted in the comments to the question, the tiles in the picture form a standard set except for an extra 5/6 and a missing 6/6. If we assume the picture to be correct, Otherwise, making the ...
ffao's user avatar
  • 21.8k
7 votes
Accepted

Monday's Unmatched Donimoes Problem

Since the 'donimoes' are limited to moving along their long axis, I believe this can be done in 12 moves as follows: Visually:
Stiv's user avatar
  • 144k
7 votes
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Place 28 dominoes in a loop

Note that So there are Now just The final answer:
WhatsUp's user avatar
  • 7,397
7 votes
Accepted

Catch 21: Lies in Advertising

The lie is: After all: Extended answer: Furthermore, as @LannyStrack points out in comments: But there's still more! Explanation of logic for deducing points in the spoiler block above:
Stiv's user avatar
  • 144k
6 votes

One rectangle, indivisible

Before the question was edited, this was a valid answer: Here's my new answer:
User4407's user avatar
  • 379
6 votes
Accepted

Thursday's Unmatched Donimoes Problem

This seemed to work. There are a couple of spots where there are disconnected pieces during a move, but IIRC that was acceptable.
Bass's user avatar
  • 77.6k
6 votes

Piece de Resistance - Two Boxes, Two Boxes of Letters

Jafe's user avatar
  • 77.5k
6 votes
Accepted

Wednesday's Dominosa Problem

Final answer: Step by step: 1: 2: 3: 4: 5:
Beastly Gerbil's user avatar
6 votes

Monday's Mirror Donimoes Problem

I have the following solution:
AxiomaticSystem's user avatar

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