The stairs in the tower of Sheik Oil Well

Did you ever wonder why medieval sultans have such beautiful daughters? Or why they have such complicated ways to select their suns in law?

1) Sheik Oil Well^*
Sheik Oil Well had two huge towers in the middle of the desert. His oldest daughter was renowned for her beauty, and suitors for her fair hand came from all the neighbouring oases.
The sheik told them: Do you see the left tower? He who can tell me how many steps the stairs have, without going up and counting them, will win her hand. I will tell you this: the number of stairs is three more than a prime number. When you would run up with 5 steps at a time, you would find that your last jump would only be 4 steps. When you divide the number of steps by 7, you would have 5 left. Oh, and the number of steps is a multiple of 19.

What is the smallest possible number of steps?

You can check your solution at here

I wish you everything that is good for the new year!

Please try to solve the puzzles on your own. You are welcome to remark on the puzzles, and I love it when you comment variations, state wether they are too easy or too difficult, or simply your solution times. Please do not state the soultions – it spoils the fun for others. I usually make the solution available after one or two weeks through a link, which allows readers to check the solution without the temptation to scroll down a few lines before having a go at it themselves.

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:

Dissections – the Greek cross

The Greek cross consists of 5 squares joined in the shape of a cross.

1) Greek cross – 4 equal parts^*

The figure above shows a strangely formed meadow between a brook and mountains. There are 4 wells in the area. The farmer died and stipulated in his will that his land would be distrubuted equally among his 4 sons; all 4 lots would have the same area and shape and contain exactly 1 well.

How was the land divided among the 4 sons?

2) The hindu problem

The greek cross as shown in the illustration to the left, is composed of 5 equal sized squares. Cut the cross into five pieces to form a square. There are 2 solutions. According to British puzzle master Henry Dudeney, the problem is over 3000 years old.

3) How many straight cuts?
Henry Dudeney next comes up with the problem:
How many cuts do you need to divide the Greek cross into 4 pieces, so that with these pieces you can form a square?

4) The Red CRoss Lassie
American puzzle master Sam Loyd recounts the following problem:

In the whole realm of puzzledom, and geometry included, there is nothing so fascinating and eminanetly scientific as the series of problems pertaining to the form of the Greek cross and its peculiar relations to the square, parallelograms and other symmmetrical shapes.
As differing from the well known mathematical problem of converting the cross into a square by the fewest possible number of cuts, attention is called to the following pretty feat of chaninging one cross into two.
It appears that one of our wounded boys in blue who was returning home after being nursed back to life by a faithful Red Cross lassie, begged the red cross from her arm as a keepsake; but she, in true sweetheart style, took her scissors and by a few deft clips, cut the red cross into several pieces, which could be fitted together perfectly so as to make two crosses of similar vsize. It is a simple but beautiful trick, and the satisfaction of guessing it will be as great as if you should win a prize.

You can check your solution here for no 1, here for no 2 and here for no 3, and here for no 4

A new puzzle is published every friday. The solution is generally published one week later. I welcome your reactions on these puzzles: are they too easy, too difficult, are there any multiple solutions? How long did you need to solve it?

Cross out

1) Cross out 5×5^**
In the square below, cross out numbers until the sum is 15 in every row and column:

2) Cross out 7×7^**
In the following square, cross out numbers till you the sum is 15 in every row and column:

This type of puzzle was probably invented by Rita Hovestad or Marenke Wiersma, editors of Sanders Brainteaser no 5.

You can check your solution here for no 1 and here for no 2

A new puzzle is published every friday. The solution is generally published one week later. I welcome your reactions on these puzzles: are they too easy, too difficult, are trhere any multiple solutions? How long did you need to solve it?

Parks

A Park puzzle has only two rules:
1) Every row, column and park has exactly 1 tree;
2) Trees are not adjacent horizontally, vertically or diagonally.

1) The stats^*

2) parks 7×7^*

You can check your solution here and
here.

Did you know?
My current customer has the nice habit of allowing its employees a certain amount of freedom. It aint as much as Google’s former 20% free time, but it does offer facilities such as posting reflective sayings. One I came across is:

If you think adventure is dangerous, try routine. It’s lethal. (Paulo Coelho)

This may be not be literally true of the body, but I believe it’s certainly true of the mind. Brains which do not regularly encounter new challenges, develop less well when young and detoriate faster when old.

One thing I consciously try to do is presenting new puzzles. And not just new puzzles, but also present a new type of puzzle. This means your brain has to start afresh with a new problem. You have to figure out new ways to tackle this challenge.
By presenting several puzzles of the same new type your brain has a chance not only to discover HOW to solve them, but also to let these ways reach the conscious state. You realize what the new tricks are with which you can solve these problems. And that is an important element of acquiring new skills (and I suspect for your brain an important part of creating new neural connections)

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.

square sums

1) 3×3
Every row and column adds up to 50
Complete the square with the indicated numbers – those who have been given are already crossed out for you.

2) 4×4
Every row and column adds up to 50

3) 5×5
Every row and column adds up to 100.

This type of puzzle was published in Cijfervaria, a publication of Sanders Puzzelboeken. As I write this, they just published issue 5. Though I missed issue 4, I see they regularly publish Soduko variants, Binairo, Triairo, hitori, and battle ship.

You can check your solution here, here and
here.

Did you know…
Learning new tasks saves brain cells – even if these tasks are more or less similar to already known tasks.

Four fours

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Using exactly four fours, create the numbers 0-30. You may use the usual mathematical operands, but not squaring, as this requires a number 2. You may use brackets.
Example: (4+4)-(4+4)=0

As always, please don’t publish your solutions. Solutions can be found after 1-2 weeks on the solution page for those who want to check their solutions, or for those who are really stuck.
But scrolling is much easier, and really spoils the fun for others.

I am very much interested in your solution times, and I welcome your remarks and criticisms. Pointing out alternative solutions is also welcome, as they point out possible problems in the brain teasers.

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

This puzzle has a long history. When I still was a teenager, my father challenged me to make all numbers 0-20 using the digit 4 exactly 4 times. Recently I shared this puzzle with some fellow consultants. Kees Krol arrived at the office one morning and announced he had extended the range all the way to 30. 🙂

Pentominosa

1) 5×12 nr 1

1) 5 x 12 rectangle^*
This 5×12 rectangle consists of the twelve different figures of 5 squares each. The original borders have been removed.
Each figure contains the letters A, B, C, D and E exectly once.
Can you find restore the borders between the twelve figures?

For those of you who are not familiar with them, here are the 12 possible pentominoes, or possible figures of 5 squares.

This type of puzzle was, as far as I know, first published in the British magazine Games and Puzzles, issue no 50, july 1976.
There is a type of puzzle where all bones from the double 6 set are laid down in a 7×8 square. Sometimes that type of puzzle is called dominosa. You can find a couple of them on my homepage, the domino plaza. Because the type of puzzle is very similar, I have christened this type of puzzle pentominosa.

2) 5 x 12 rectangle^*

3) 5 x 12 rectangle^**

You can check your solutions at here, here and here.

Please do not list the solution(s). In all other respects, I welcome discussion, listing alternative solutions, and I espoecially welcome your solution times, as that helps me to get an impression of the difficulty.

Review metal puzzles from TTIE and Eureka

This is one of three reviews to be published this summer while i’m away on holiday,

This post is about metal puzzles that I received for my birthday and fathersday. My thanks go to the family members who donated them.

The metal puzzles from T.T.I.E, PO Box 62 2420 AB The Netherlands are a series of sturdy metal puzzles. They come in grey boxes, which are mostly of a standard size.

Many of the smaller ones look like standard problems, consisting of 1 twist. I was not able to find their website, zo it is probably not a very big firm.

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Two of the puzzles I received are more original, they come from Eureka! 3D puzzles. The one with three rings is nice, I havent seen it before, though all the elements are very standard.

The puzzle which I christianed “Double E” is a nice one. It took it with me to the office, where my puzzle friends quickly solved it. Then I twisted them into each other again, and somehow we have been unable to separate them again.

You can find the website of the supplier at http://www.eureka-puzzle.eu/eureka, though they only sell to retailers, and dont seem to sell to individuals.