Category Archives: Geometry

Domino – lay out that set

Dutch puzzle designer Leon Balmaekers contacted me recently and told me he had written some booklets with puzzles for highly gifted children. The booklets are in Dutch, and contain a variety of puzzles. The highly gifted children in a classroom can make some of these puzzles when they have completed the normal exercises in a breeze.

One of the puzzle types uses a normal 0-6 domino set. Look at the figure in problem 1. In contrast to dominosa, the domino puzzle type most often used, the borders are clear, but the digits are missing.

Problem 1.**/*****
The numbers along the sides are the sum of the pips in the respective rows and columns. It is up to you to figure out which domino should go where. Normal domino rules are followed: whenever two bones lay end to end, the numbers are equal.

For your convenience, here is a complete double 6 set:

You can check your solution here

Problem 2**/*****

You can check your solution here

Problem 3***/*****

You can check your solution here

A new puzzle is published at least once a month on the first Friday of the month. Additional puzzles may be published on other Fridays.


This week we have a plane and simple geometry problem

1) The rectangle**/*****

The rectangle contains three identical circles. The two smaller, shaded rectangle touch the sides of the rectangles and touch the circles. What percentage of the area of the large rectangle is covered by the two small rectangles?

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 5 stars.

Geometry – or is it?

1) Three squares**/*****

On twitter I found the account of a very kind and smart lady called Catriona Shearer, who poses a lot of very nice and original math problems. One problem is reproduced here with her permission. In the figure above, the sides of the three squares are three consecutive integers. The length of the black line is 4√10.
What’s the total area?

You can check your solution here

2) Four squares***/*****
The puzzle above inspired me to the following puzzle:

The length of the sides of the three smaller squares are all natural numbers – integers if you prefer that term. The length of the side of the big square is 6√10.
What is the size of the three small rectangles?

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 5 stars.

You can check your solution here


Rikudo**/***** essentially are made up of a (partially hidden) string of the numbers 1 to N embedded in a figure consisting of hexagons.
I must admit I never figured out how to efficiently draw a couple of hexagons, so I’ll use squares arranged alternating in adjacent rows – the net result is identical in terms of the number of adjacent borders.
Usually, the number 1 and the highest number are given. Sometimes the author puts a dot on a border to indicate that the adjacent numbers differ by 1.

Solving strategies

  1. A straight line between two given numbers, with the length of the line equal to the difference between the two numbers

  2. Two adjacent hexagons have numbers which differ by two

  3. No dead ends

    Though there are several routes from 6 to 10, only 1 will fill the red square.

You can check your solution here


Pluszle® is the trademarked name of a new type of number puzzle I encountered in the book/magazine shop at The Hague CS. I didnt want to buy it, but today my wife bought me a copy. The rules for the puzzle are elegantly simple. The grid is filled with numbers, and you have to cross out numbers till the sum of the remaining numbers equals the numbers in the right and bottom margins.

1) 5×5 nr 1*/*****

2) 5×5 nr 2**/*****

3) 6×6 nr 2**/*****

Priced at 4,95 euro and containing 375 puzzles it doesn’t sound like a bad deal. The main problem seems to me that the first part of the booklet contains 3×3 and 4×4 puzzles. In my humble opinion, these could have been omitted. Just this morning I was tweeting about education, automation of arithmetic, and differentiation in exercises for different students. Maybe I would have loved it to get puzzles like these at primary school as extra exercises.
The booklet is produced by Pluszle BV in Leusden, and outsider in the Dutch puzzle magazine world, which is dominated by Denksport and Sanders puzzels. Their website at mentions apps for the I-store and the android store, but I must admit I didn’t try the app.

Another, albeit smaller problem, is that the main variation is the size of the grids: the larger the more complex. It isn’t too difficult to create similar problems with multiplication:
4) 5×5 nr3*/*****

Another variation I can think of is a 4×4 grid with subtraction: cross out two numbers in every row and column so that the difference is the number in the right or bottom margin.

There is an even more puzzling form, but I think I reserve that for a subsequent post.

Now my words above may sound like a negative judgment, but I do not intend them to be that way. The larger sizes 6×6 and above, do offer a fair agree of difficulty.

Solution strategies
There are several solution strategies, here are the main ones:

(a) 8 can not be there, >5
(b) 3 can not be there, not in any combi
(c) 6 must be there, else you can not add up to 15
(d) all numbers must be there

Plastic snake

Last week I purchased another snake. It is not the first one I obtained, and if its price wasn’t ridiculously low at 4 euro, it would have remained in the shop at The Hague (or was it Utrecht?) Central station. The producer is listed as Clown Games.

You can read about the previous one here.

The packaging consisted of plastic, which I had to cup open.

At 4 euro it was so cheap that wondered if it would fall apart before i finished the booklet with examples, but it actually turned out to be sturdy, and even to a degree where it requires some force to turn.

The little instruction leaflet contained just 4 figures:

These can indeed be constructed:

There are numerous figures one can make with the snake. Credits for the following figures mostly go to my wife Jos and our daughter Margreet:

Maze with numbers

This week I’d like to present a new type of maze.

Somewhere among the concept of this blog is a concept about mazes, their history, their shapes and their applications. In my small library are at least two good books about mazes. But here’s a new type of maze. Smaller versions may be suitable in the class room, while this shape and size are aimed at adults.

Your task? You see the two big 7’s? Find your way from one to the other, by moving vertically or horizontally, through squares which are a multiple of 7. Sounds easy, does it?

Here’s your exercise:

You can check your solution here

New puzzles are published at least twice a month on Fridays. Solutions are published after one or more weeks. You are welcome to discuss difficulty levels, variations and alternate solutions, but plz. don’t publish the solutions.