# 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

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.

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.

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:
* http://www.spotthedifference.com/ : spot 4 differences in a couple of images, allowing you to give up and try again later. Differences are both small and large
* http://spot-the-differences.com/: 5 differences, all well visible, timed.
* http://www.coolmath-games.com/0-spotthedifference2: timed, retry option. Alas flash seems required.
*

# Shikaku

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.

Example:

The 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

2) problem 7×7

3) problem 12×12

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

# Number squares

1) Number square*
Find the missing number:

solution: 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:

``` BEER
BEER
BEER
WINE
WINE
WINE
WATER
WATER
WATER
-----+
DRINK
```

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:

# Pattern codes – circles

1) Circles**

Which code belongs at the question mark?
If you wish, you can peek at a hint

I have long suspected that there is a strong connection between mathematics and puzzles. Proving such a relation according to the scientific standards is of course another matter. It was nice to read that a study by the University of Chicago found that puzzle play helps boost Learning Math-Related skills in children between ages 2 and 4.

# Masonry

The advertisement flyer of the contractor showed me several examples of masonry, with bricks in two colours: brown and yellow.

Which code should be substituted for the question marks?

You can look up a hint

Puzzlers are likely to value their brain power. So I’ll take this opportunity by passing on some research results: walking increases your memory

# Pattern codes – signalling people

1) Signalling people**
Have you ever seen the people on an aircraft carrier, or in the mountains, signalling an helicopter to get down at a specific point?

This puzzle is inspired by those people and signals.

solution

Did you know….
Body language provides a much better cue than facial expressions when judging if a person has just gone through severe emotions?
See here for more details.