Category Archives: Recreational mathematics

Matchsticks patterns


What letter combination goes to the question mark?

You can check your solution here

If you like this puzzle, why don’t you have a look at my e-book?

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Matchsticks – a diamond


Have a look at at this diamond – it is made up of 10 triangles.

Your challenges are:
1) 8 triangles**/*****
Move 4 matchsticks and have 8 triangles

2) 7 triangles**/*****
Move 4 matchsticks and have 7 triangles

3) 6 triangles**/*****
Move 4 matchsticks and have 6 triangles

4) 5 triangles**/*****
Move 4 matchsticks and have 5 triangles

You can check your solution here

New puzzles are published at least twice a month on Fridays.

River crossing


In the past I published several posts on river crossing puzzles. I think together they are the most extensive resource on river crossing puzzles on the web.

I used the week between Christmas and New Year to look for apps. To my surprise, there was just one, and it held just a few puzzles. Well, it did in spire me to:

1) The Autists and the Lazy.
Six people want to cross a river. They have a boat which can hold only 2 people at a time.
* Two of the six people are autists. They don’t want to be in the boat with any one else, though they don’t mind being on the same shore.
* Two of the people are outright lazy, and don’t want to row.
* The remaining two people are normal.
How many crossings does the boat have to make?

You can find the old posts here:
* Man, wife and kids – river crossing 1
* The farmer, the wolf, the goat and the cabbage – 2
* Three couples – river crossing – 3
* Bigamists – river crossing – 4

New brainteasers are published twice a month on Fridays.

You can check your solution here

Matchsticks – 3-7=8?


1) 3-7=8?***/*****
Please correct the following equation by moving one matchstick:


1) 3-7=8?***/*****
Please correct the following equation by moving exactly two matchsticks:


You can check your solutions here

Originally I had only puzzle nr. 2. I’d like to thank reader Mr. Haubrich for pointing out nr 1.

New puzzles are published at least twice a month on Fridays.

Happy new year!


What do you read when you superposition these three figures?

You can check your solution here

New puzzles are published twice a month on Fridays. Solutions are revealed one or more weeks later.

This puzzle was inspired by the “100 doors” app, and by the Dutch translation of 1000 casse-tete et enigmas by Piere Berloquin.

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.

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.