Category Archives: Recreational mathematics

Christmas 2017


Dominosas are puzzles where the dominoes have been shuffled and turned face up. All the numbers are given, but the borders between the dominoes are not given – these have to be solved by the reader.
I used to publish quarterly on them at my site domino plaza.

Usually a 6×6 set of dominoes is used, though larger or smaller sets can be used.

Here are two examples:
1) The christmas bauble**/*****


2) The church****/*****


You can check your solution here

3) Solving strategies
a) Counts
Make a count of how often all combinations appear. To do so, list all dominoes and how often they appear in the puzzle:
0-0: 2
1-0: 3
1-1: 5
2-0: 2
2-1: 1
2-2: 3
and so on.
This will give you the position of 2-1. Mark the borders on the printed puzzle.

b) Cross off deleted connections



Continuing the above example, it is easy to jump to a conclusion about 3-3, but before that we have some bookkeeping to do. Identifying the domino severed a number of links. In our example the severed links are the 3-1, 6-1, 2-0, and 5-2. When we update our list above for these severed links, we find that the number of 2-0 combinations is now reduced to 1, giving another domino.

c) Unique positions.



In this diagram, it is easy to see that in the top left position, only-the 3-3 is possible.

d) Block impossible links
Identifying the 3-3 domino blocks the link between all other 3-3 combinations:



This in turn, will in some situations trigger another situation like in step c)

New puzzles are published at least twice a month on Fridays. Solutions are usually published after one or more weeks.

External links:
https://www.puzzle-dominosa.com/ – play them online
https://www.chiark.greenend.org.uk/~sgtatham/puzzles/js/dominosa.html – another online game site
http://medmunds.github.io/puzzles/dominosa.html – 3rd in line play
https://play.google.com/store/apps/details?id=com.oxothuk.dominosa – android app
http://www.mathematica-journal.com/2014/10/three-ways-to-solve-domino-grids/ – three ways to solve them.

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Matchsticks – hexagon


Last month we looked at some hexagon matchstick puzzles, and this month features some more.

1) Move 4 matches**/*****
From the figure above, move 4 matchsticks so that you have 4 triangles on unequal size.

2) Move 4 matches***/*****
From the figure above, move 4 matchsticks so that you have 6 triangles again.

You can check your solutions here and here.

New puzzles are published at least twice a month on Friday. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.

Matchsticks – hexagon


Matchsticks puzzles are over a century old, but seem to go through a revival with several apps featuring them.

1) Move 3 matches**/*****
From the figure above, move 3 matchsticks so that you have 4 same sized triangles.

2) Move 4 matches***/*****
From the figure above, move 4 matchsticks so that you have 4 same sized triangles.

You can check your solutions here and here.

New puzzles are published at least twice a month on Friday. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.

Matchsticks – the T


Have a look at the following figure:
matchsticks-t-2017-01-20-exercise


You can easily check that 16 matches form 5 squares.

Move 2 matches**/*****
Move 2 matches to create 4 squares

You can check your solution here

Move 3 matches**/*****
Move 3 matches to create 4 squares

You can check your solution here

Move 4 matches**/*****
Move 4 matches to create 4 squares

You can check your solution here

New puzzles are published at least twice a month on Friday. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.

Matchsticks – triangles (2)


3 triangles***/*****
Move 2 matchsticks to get 3 triangles:

matchsticks-triangles-2016-12-14-nr-2-exercise

You can check your solutions here.

New puzzles are published at least twice a month on Friday. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.

Matchstick – triangles


Surface***/*****
These 6 matches enclose an area with size 2 (2 standard triangles).
Rearrange them so that:
a) they enclose an area of exactly 4 triangles
b) they enclose an area of exactly 6 triangles

matchstick-triangles-2-2016-12-14-nr-1-exercise

You can check your solutions here.

New puzzles are published at least twice a month on Friday. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.

Matchsticks – a list of apps


Recently I downloaded a couple of matchstick puzzle apps on my android phone and on my ipad. Below you find an incomplete list of android apps with matchstick puzzles.

Here is a short list:

Name Publisher Type of puzzles Remarks
Matchstick puzzle Uysal Mehmet Digital Puzzles Minimalistic interface. It baffled me at first. I didn’t see hints or solutions, but that doesn’t mean they aren’t hidden somewhere.
Puzzles with matches Celtic Spear Digital matches, triangles and squares Well designed interface. Puzzles gradually increase in difficulty. Recommended!
Matchstick puzzles Gamophonica Squares At level 6, I found a symmetrical solution is not recognized. Interface is clear. Same on levels 7 & 8, and probably on subsequent levels too. I informed the publisher and they responded quickly to my email, so I trust this problem will be resolved when you read this (written dec 2016).
Matches Puzzle Game Bojan Klabjan Squares, triangles, numerical digits Original interface. Well designed. Recommended!
Matchstick Puzzle Alt-y Digital numbers Both moving and 1 and 2 matchsticks.
Amazing matchsticks Network Game&utility ? I skipped this one, as it asked 4 types of access which I deemed unnecessary
Matches Puzzle 2016 Fitapp Inc Digital numbers Both 1 and 2 matches to be moved. If you are stuck, solutions can be bought with in-game money.
Math puzzle with sticks LogiGames Digital numbers Beautiful interface, but I miss a clear indication of how many matches I have to move. Or maybe it is always just 1 match.

I admit I’m not even halfway through the list.

Anyway, here are two puzzles.
Problem 1*/*****
matchstick-digital-numbers-2016-12-29-nr-1-exercise

Problem 1***/*****
matchstick-digital-numbers-2016-12-29-nr-2-exercise

You can check your solutions here and here

New puzzles are published at least twice a month on Friday. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.

Matchsticks


1) Move 6 matches**
Consider the following figure:
Matchstick 3x3 move 6 matches exercise

Now move 6 matches so that you have 4 squares.

You can check your solutions here

New puzzles are published at least twice a month on Fridays. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to three stars.

Sliding coins puzzles


There are many beautiful puzzles with coins. I don’t mean those which have to do with the value of the coins, but with the puzzles in which you have to move coins around. Neither do I want to discuss the puzzles which are about arranging coins in a straight line. These are often represented as planting trees in a row, and I discussed them here.

While on holiday in France this summer, I bought two puzzle booklets in the ‘aires’, the road stops with a restaurant, a gasoline station, a toilet and some more. One of them, ‘Best of jeux de vacances, 700 jeux’ by Pascal Naud, contained at least two of them, both classics, so I can reproduce them here without encountering copyright problems.


  1. 5 coins in a row*/*****

  2. Move 1 coin so that there are 5 coins in both rows,
    5 coins in a row exercise

    You can check your solutions here

  3. Pyramid*/*****

  4. Turn the pyramid upside down by moving 3 coins.
    Coins pyramid exercise

    You can check your solutions here

Many similar (and much more difficult) problems can be found on youtube.


  1. Move 3 coins to make a circle







At the beginning of the summer I was asked to become one of the elders in our church. It unfortunately means that I am not able to keep up the rate of a puzzle a week. Having a fair collection of posts in stock, I was able to keep posting puzzles weekly. But I’ve about run out of puzzles in stock. So be prepared there will be 2 puzzles a month from now on till the end of the year.

You are still welcome to comment on puzzles here, or to buy my book.