Sliding block puzzle with 4 pieces

The sliding block puzzle on this photo was invented by James W. Stephens; it is called the simplicity puzzle. The aim is to move the three square piece from the bottom right corner to the upper left corner. My colleague Edwin Santing produced it using the 3D printing facilities at shapeways.com, and google sketchup for the design.

Mike W. Stephens has his own puzzle site, called puzzlebeast. He specializes in sliding block puzzles, and his site is well worth a visit.

Beautiful as this puzzle is made, it is easy to make a temporary one yourself from cardboard. There are many, many shunting puzzles possible, and I intend to get back on this topic later.

Cubes

Cubes are wonderful things. With six side surfaces, eight vertices and 12 edges, they are highly symmetrical. There are 11 ways to flatten a cube into a plane by cutting the edges. Here are 6 of the 11 ways:

Can you tell which cube is different? You can ignore the orientation of the letters – they are merely for identification. The symbols have been added for those readers who are colourblind.

If you are puzzled, we have a solution for you.

Did you know?
The subiculum plays a role in spatial navigation, mnemonic (symbol) processing. You probably already understood that this puzzle challenges the 3D representation facilities of your brain.

Playing with numbers – quickies

The next two problems are variants of easy problems from the Dutch 2008 Mathematics Olympiad.
1) 2016^*
What is the smallest integer number that, when multiplying its digits, gives 2016?

2) Odd numbers ^*
Multiply all numbers between 1913 and 2012 (including 1913 and 2012). What is the last digit of the product?

You can check your solutions at 16 and 26 respectively.

Books

1) books^*
The professors assistant entered the office room of the professor and noticed that the professor had not only labeled the plants as shown in a previous post, but also his books. Only a new book on his desk was not yet labeled. Can you help him out?

You can look up hint here.

As you may have noticed I like this type of puzzle. Though I am no brain expert, i think you need to active different parts of your brain, and though I’m no expert in the field here’s a list of those parts of the brain which i think will be utilized while solving these puzzles:

• According to research by J. R. Binder and others, the Angular gyrus was used heavily when processing abstract keywords. Finding the correct abstract concepts play an important role in these puzzles.
• Prefrontal Cortex: used for: planning, reasoning, and judgment. Once you have an idea which properties of the objects play a role in the codes, you will need deductive reasoning to check that. Deductive reasoning activates the left frontal lobes, as researched in a meta study in 2011 by Jérôme Prado, Angad Chadha, and James R. Booth.
• The Occipital Lobes are used by visual activities, and as these puzzles are highly visual the solver needs to use this part of his/her brains.
• The inferior frontal gyrus and middle temporal gyrus are utilized according to research by Jing Wang, Julie A. Conder, David N. Blitzer, Svetlana V. Shinkareva.
• Corpus Callosum: This allows information to move between the left and right hemispheres of the brain and is thus a very important integrative structure.

Next weekend we hope to be away a few days, so the puzzle may be later than usual.

Fractions

1) Which Fraction is missing?^*

You can check your solution.

Camel inheritance

1) How many camels?*
The sheik has died. When the Mullah read the will, he found that the sheik had left each of his five sons 1/6 of his camel herd, while his only daughter in an act of sheer discrimination inherited only 1/8th of the herd.
The mullah solved it for the kids without butchering a camel.
How many camels did the sheik have?

You can check your solution.

The puzzle above is a new one, and of course derived from the following classic:
2) 17 camels and three sons**
The sheik has passed away. When the mullah opens his will, he finds the sheik has left 1/2 of his camels to his oldest son, Achmed, 1/3 to the second son, Harim, and 1/9th to poor Bahari, the youngest. Now one of the sheiks camels had died in an accident a month ago, leaving only 17 camels to be divided.
How did the mullah divide the camels without butchering one?

This puzzle is based on a problem which according to some was first posed by Gaston Boucheny, “Curiosités et Récréations Mathématiques”. Paris, 1939. The French ed. of MRE says it is a problem of Arabic origin, while Kraitchik, Math. des Jeux, says it is a Hindu problem. The claim attributing the puzzle to 1939 seems wrong to me, as Sam Loyd and Henry Dudeney posed the problem in the Strand magazine years earlier. In fact, this puzzle was included in Henry’s puzzle book: “536 Puzzles and Curious problems” as number 172.

There is a hint.

3) The seventeen horses**
“I suppose you all know this old puzzle” said Jeffries. “A farmer left his seventeen horses to be divided among his three sons in the following proportions: one half to the eldest, one third to the second, and one ninth to the youngest. How should they be divided?”
“Yes, we all know that”, said Robinson. “But it’s impossible. The answer given is always a fallacy.”
“I suppose you mean,” Progers suggested, “the answer where one horse is borrowed, so that the division can be done without butchering a horse, the sons receive9, 6 and 2 and the extra horse is returned”.
“Exactly!” Robinson replied “And each son receives more than his share.”
“Stop!” cried Benson. “If each man receives more than his share, the total must exceed 17 horses, but 9, 6 and 2 neatly sum up to 17.”
“That indeed looks queer”, Robinson admitted, “but 17/2 is 8,5, not 9. so the oldest son receives more than his share. And it’s similar for the other sons. The thing can’t really been done”
“And that’s where you all are wrong”. Jeffries stated. “The terms of the will can exactly be carried out, without any mutilation of a horse.”
To their astonishment, he showed them how it was possible.

There is a hint.

Oh, the image at the top of this page is the coat of arms of Zurich, available under GFDL license and created by Ronald zh.

Pattern code post-its

1) Post-its^*
You know those super busy people at the office? Their desk is full of yellow post-its. Every office seem to have at least one such person. One fellow worker had a system to code their priority. Can you find his system?

You can look up a Hint

Coffee with milk, please

Tanya Khovanova publishes an irregular but excellent blog about math problems. Of Russian descent, she often uses Russian sources, which are otherwise not very accessible in the Western world. The next problem comes from her blog, and has the Moscow 2011 mathematics olympiad as origin:

1) Coffee with milk, please^***
1) Coffee and milk^**
In a certain family everyone likes their coffee with milk. At breakfast everyone had a full cup of coffee. Given that Alex consumed a quarter of all consumed milk and one sixth of all coffee, how many people are there in the family?

The above problem would go into the class of problems for which you have n equations and n+1 unknowns. Here’s a classic in this category:

2) A farmer went to the market^*
A farmer buys 100 animals for 100 dollars but lost his receipt. Cows are $10 each, pigs are $3 each and chicks are $.50 each. How many of each did he buy?
This puzzle is a ‘classic’, but I don’t know its source. If you do, I’d welcome this information!

When you solved both, you will notice that the solving methods of the two puzzles are totally different.

You can find hints at 126, 116 respectively.

patterns – ballpoints

ballpoints
Which code goes to the question mark?

You can look up hint here.

Triangle sums

Each cell in this triangle is the sum of the two cells below it. Can you complete them?
1) triangle 1^*

				75
			43		.
		28		.		.
	18		.		.		.
.		.		.		.		8

I first encountered this type of puzzle in the Dutch translation of “One minute puzzles”, published by Arcturus Publishing Limited, London. This book published the numbers in circles, and all puzzles had the difficulty level of the one above, where there is always at least one cell which can be calculated with a simple addition or subtraction.
I replaced the circles with the pyramid pictured above, and in the following puzzles you will find an extra difficulty level introduced.

2) triangle 2^*

				.
			.		.
		18		.		15
	.		.		.		6
7		.		.		.		2

3) triangle 3^*

				115
			.		.
		19		.		36
	.		.		.		.
7		.		.		.		8

4) triangle 4^*

				80
			.		.
		18		.		24
	.		.		.		.
.		1		.		4		.

This type of puzzles exercises the parts of your brain which performs the arithmetic. If I interpret this article correctly, that is the horizontal segment of the bilateral intraparietal sulcus (HIPS), together with the precentral sulcus and inferior frontal gyrus.

You can check your solutions at solution 221, solution 231, solution 241, and solution 212.