Category Archives: Puzzles

Geography (2)

On June 15, I published an 8 question test with alternate geography questions. Here is a short bonus. As in the previous test, the questions are replicated for several continents
After writing it, I discovered “World Geography” in the Android play store. It featured a series of different question types, some traditional, others less common, such as:
a) With a map of the continent shown, and one country highlighted, what is the name of this country?
b) With just the silhouette of the country shown, what is the name of this country?
c) What is the capital of a country?
d) Of which country is this the flag? (flag depicted)
e) how many inhabitants does a country have (<1 million, <10 million, <100 million, >100 million)

Here are some questions. Unlike my previous quiz, the questions are not by continent, but are worldwide.

1) Which islands are depicted?

2) Name the countries which belong to these flags:

3) Rank these cities from North to South:
Beijing, Berlin, Moscow, and Washington

4) Rank the following countries according to number of inhabitants:
Canada – Bangla Desh – France – Egypt

5) Rank the cities from least to most annual rainfall
Los Angelos – Washington – Madrid – Cairo – Tokyo

6) In which countries do these rivers have their origin?
Amazon – Nile – Donau – Mekong

I would like to thank user Rei-artur of wikimedia commons for releasing the first of the island maps above.

You can check your solutions here. I strongly advise you to write down all your answers before checking them.


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


When I got geography at primary school the main things I remember is that I had to learn which provinces we had in the Netherlands, and which towns are located where. At secondary school, the scope was broadened to Europe, the rest of the world. Of course, the location of major mountain ranges and rivers was included, again the form of “What is the name of this mountain range?” or “Where is river X?”.

This weeks puzzle is not so much a puzzle as an alternative geography test. If you are a geography buff, try your hand at this! The first question is a traditional question, to get you going, but the remaining questions require you to work with your geography knowledge in an unconventional way.

(Nearly) Everybody knows a lot more about the area close by than about countries far away. For this reason this questionnaire differentiates between USA, Dutch/European, and other countries. For these last, I welcome additions in the remarks section at the bottom of this post.

Rule: answer from your head – do not consult an atlas or wikipedia.

1) What is the capital of the State Arkansas?

2) Which states border the state of Missouri?

3) Mention three state capitals that start with the letter “D”.

4) Through which states does the river Rio Grande flow?

5) Which state has a larger surface: Wisconsin or Wyoming?

6) What is the largest (in terms of population) city in the state Alabama?

7) Which primary interstate highway serves the most states?

8) Geographical knowledge should also encompass knowledge not directly related to your home country. Which countries does Bolivia border in the west?

1) What is the capital of Ukraine?

2) With which countries does Austria share a border?

3) Mention 3 capitals starting with a B?

4) Through which countries does the river Donau flow?

5) Which country has a greater area, Austria or Czech republic?

6) Which capital has more inhabitants, Berlin, Londin or Paris?

7) Mention 5 countries in Europe with mountains above 3000 meters.

1) What is the capital of Cambodia?

2) With which countries does Afghanistan share a border?

3) Mention 3 capitals starting with a “D”

4) Through which countries does the Mekong river flow?

5) Which country has a greater area, Thailand or Iraq?

6) Which capital has more inhabitants: Manila or Riyadh?

7) What is the length of the longest highway in China?

1) What is the capital of Noord Holland

2) Which provinces border Gelderland?

3) Noem 3 steden met meer dan 100.000 inwoners die met de letter D beginnen

4) Door of langs welke provincies stroomt de rivier de Maas?

5) Welke provincie heeft een groter oppervlak: Drenthe of Limburg?

6) Welke stad in Gelderland heeft de meeste inwoners?

7) Door welke provincies loopt de A4?

You can check your solution here

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

Origami Manifold Puzzles

The September issue of the Dutch magazine Quest came with a small origami puzzle booklet. It contains 8 puzzles. The puzzle in each case is to fold a square piece of paper, such as depicted below, in such a way that one side is black and the other side is white.

There is a book published by “The Incredible Company“. You can freely download a free pdf with 5 puzzles from there site. The book does not seem to mention an author, though I suspect the author is Jérôme Morin-Drouin. Play testers were two people named Caro and Felix.

To solve the puzzles below, print them, cut them and fold them such that the result is a sqiuare, white on one side and black on the other.

Puzzle 1*/*****

Puzzle 2*/*****

Puzzle 3*/*****

No solutions will be given.
Credits go to Quest for pointing out this puzzle type, to the incredible company for coming up with the idea and to my daughter Margreet for puzzle number 2 above. NUmbers 1 and 3 are my own work.

Spot the differences

Once a month, or once every other month, I try to take a more in depth look at a puzzle type. This month I want to have a look at the “spot the differences” puzzles. This is a pretty popular type of puzzle, Bing turns up at least 4 different websites and the google playstore has at least 10 apps. URLs of the websites are mentioned at the end of this article. The trigger for this post is my recent acquisition of a magazine “zoek de verschillen” (find the differences) by Denksport, the largest puzzle publisher in the Netherlands.

1) Spot the differences
ZLimburg DSC_0979 original

ZLimburg DSC_0979 diff 0.20

Try to find all 15 differences!
(The picture has been taken in the Netherlands, in the tourist town of Vaals).

You can check your solutions here

While making this puzzle, trying my hand at some of the puzzles in the magazine, and browsing around on the web, I noticed there are several types of changes:
1 – an object appears in one image and not in the other. An example is a traffic sign that has an arrow in one image and no arrow in the other. The object often is small.
2 – the object is present in both images, but with different colors. For instance, if you have a dish with colorful sweets, one of the sweets has been changed from green to orange.
3 – the object is present in both images, but in one image it is longer, shorter, wider or narrower than in the other. In one of the puzzles in the web, I noticed a garbage can, attached to a pole, reached to the pavement on the left imgae while in the right image it was a foot above the pavement.
4 – the object is present in both images, and the object is identical in both images, but in a different spot. For example, that crow on the roof is sitting near one end of the roof or in the middle.

What makes a puzzle tough? Which differences are hard to spot? I could not find any scientific research on this topic. Generally, I’d say that small differences are harder to spot than big differences. But some differences seem to be ignored by the eye or mind, even though they are not particularly small. A change in a background is often harder to spot than one in the foreground. Changes to the top of an object seem to be spotted more easily than changes to the bottom.

2 identicals
A second format that the afore mentioned magazine applies is that of 6 copies, and you have to find the 2 identical copies.

DSC_2102 original zonder persoon BL DSC_2102 original zonder persoon BR
DSC_2102 original zonder persoon ML DSC_2102 original zonder persoon - MR
DSC_2102 original zonder persoon OL DSC_2102 original zonder persoon OR

The abundant availability of digital photos has greatly enhanced the possibility for everyone, both amateur and professional, to create these puzzles. I don’t have photoshop, but MS paint served me well during the creation of the puzzles above. Before the age of electronic manipulation, the images were often handdrawn. You can find one on the english language wikipedia.

You can check your solutions here

3) Subdivisions
A large photo is subidivided into small rectangles, with rows and column labelled. A few of the rectangles are copied below the photo and the puzzler has to find out which small rectangle they correspond with.
shells with lines

shells cutout 1
shells cutout 2

What are the coordinates of the two cut outs?

You can check your solutions here

4) Cutout
A rectangle is cut out from a photo and displayed below it. Several other sections are copied below the photo, and the puzzler has to find out which is the cut out which fits into the picture. The cut outs are tilted, and I currently lack the skills or tools to do this for you.

5) Links
Here are some of the links I found and which work:
* : spot 4 differences in a couple of images, allowing you to give up and try again later. Differences are both small and large
* 5 differences, all well visible, timed.
* timed, retry option. Alas flash seems required.


Shikaku puzzles are puzzles which can be found in some magazines. They were invented by Nikoli, a Japanese puzzle firm. Allthough they can be drawn in black and white, the colored versions seem to be more popular. There are several websites offering them – see below They are also known as Shikaku ni Kire, rectangles, Divide by Squares and Divide by Box.

The basic is a square or rectangle which has been subdivided into rectangles. The border lines are not shown in the exercise – this is what the solver has to find out. The sizes of the rectangles are given as clues.

shikaku 5x5 exercise

The solution:
shikaku 5x5 nr 1 solution

As you can see in the examples above:
(1) Only rectangles are used;
(2) Every rectangle has exactly 1 square indicating its size;

Here are some puzzles with them:
1) Problem 6×6

shikaku 6x6 nr 1 exercise

2) problem 7×7

shikaku 7x7 nr 1 exercise

3) problem 12×12

shikaku 2015-03-05 12x12 exercise

There are several apps for your android smartphone or ipad around. Sites which offer shikaku puzzles are:


You can check your solutions here, here and here

Inspector Smart on the Isle of Thieves and Liars

After his adventure on the island of Koaloao, Inspector Simon Mart traveled on to the second island in the Logico archipelago, Lotl Ire Esa.

The population of this island, he knew, was very peculiar; it consisted of two distinct groups, each with his own rigid disposition, and the inspector suspected it was a genetic mutation.
One group on this island was called Thieves: they had an uncontrollable tendency to steal, but they would always tell the truth. The other group was called Liars, they never stole anything but would always lie.

1) The scepter of dignity
After checking into his hotel, he had gone straight to the police headquarters in the capital. In the case before him, there were two suspects, Peter and Paul. The crime under investigation was the theft of the Scepter of Dignity, a rod made of used matchsticks, and dating back to 1997.

Peter: Paul is a Thief. But he did not steal the scepter.
Paul: Peter is a Thief. And Peter stole the scepter.
It was already certain that one of the two had stolen the scepter. Who is guilty?

If you wish you can check your solution.

Strong drinks

1) Drink**
This weeks puzzle is a cryptarithm, one of the type of a non unique list:


Solve this with A less then B.

It goes without saying that I strongly advice you not to drink any beer or wine when solving this puzzle. And while we’re on the topic: though a glass of wine is reported to be healthy, be aware that any large amount of alcohol destroys a number of braincells, and that brains which are not full grown may suffer more damage from alcohol than full grown brains.

(Solution: 60)

Magic snake

The magic snake is a plastic puzzle manufactured by Shuo Yi toys factory, Shang Hua town, China. It is constructed of a series of half cubes, cut diagonally, and connected with what loooks like a string. I don’t know the price, it’s a present given by “Black Pete”.

The packaging looks cheap, and the back carries the images of 9 3D figures which can be constructed with it.

Here are some more figures which you may wish to create:
magic snake flower mini 20131201_203705

magic snake stairs mini20131201_190442

magic snake knot white mini 20131201_130846

magic snake knot green mini 20131201_130547

magic snake cylinder mini 20131201_123846

magic snake cobra 20131201_121013

magic snake rectangle mini 20131201_092023

figuren en kerst 001

figuren en kerst 009

figuren en kerst 011

figuren en kerst 012

figuren en kerst 006