Lines and spheres

What code goes into the question mark?

You can check your solution at here

A prime maze

Mazes are very old and very diverse. I hope to write about mazes in eneral another time, but here is one variation.

Go from 1 the upper left corner to the bottom right corner with the following rules:
1) When you move from one square to the next, add the number in between
2) Every new number must be a prime number

For those of you, a prime number is a number of 2 or more which can only be divided by 1 and by itself. Thus 2, 3, 5 and so on are prime numbers, but 4, 6 and 9 are not.

I found this type of puzzle in one of the old Dutch math olympiads.

You can check your solution at here

Please try to solve the puzzles on your own: your self confidence will grow. 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.

Color grid (1)

What number goes into the cell with the question mark?

1) Color grid^*

You can check your solution at here

Please try to solve the puzzles on your own: your self confidence will grow. 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.

You can find more puzzles of this type in one of our free or paid upcoming e-books on Logic puzzles.

Glasses of water and wine

At atheneum (high school), my mathematics teacher was drs. Hofman. One day in class he posed us the following problem:

I have a glass of wine and a glass of water. Both glasses are of the same size, and contain the same amount of liquid.
Now I take one teaspoon from the glass of wine and put it in the glass of water. After mixing it with the teaspoon, I take a teaspoon from the glass of water and put it in the glass of wine.

Now, is the proportion of wine:water in the wine glass bigger, smaller or equal to the proportion of water:wine in the water glass?

While in class I saw the answer, but somehow managed to say it wrong. I don’t think drs. Hofman invented the problem, as Vladimir Arnold mentions this problem in an interview with S.H. Lui. In have very kind memories of mr. Hofman, he was always available for assistence or advice, and managed to challenge us without us realizing we were being challenged. He was also remarkable in another way: He managed to have three marriages days with the same woman. Thrice he proposed to her, thrice she accepted, but the first two times she said “no” on the morning of their marriage day, according to that I heard because she didnt have the courage to face that Big day.

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.

When you have solved this puzzle, you can check your solution here

The Babuschka and the pearls

Before going home, Inspector Simon Mart visited a pearl shop on the island of KoaLoao, where every native was either a TruthTeller or a LieSpeaker, he decided he really had to take home a souvenir.

He looked around in one of the local pearl shops. It was not very large, but his eye fell on a nicely crafted Babuschka – one of those russian dolls where, when you open it, it contains another similar doll, which, when you open it, ok, you get it.
This babuschka contained 3 smaller dolls, and had six small pearls inlaid for the eyes of the dolls. He picked it up and weanted to buy it, but his eye fell on a pillow with 4 beautiful large pearls, some entire white, some entirely black. He remebered that all pearls on this island were either black or white.
“How many of these large pearls do you have?” Simon asked, interested.
“Not very many” the shopowner asnwered. “My neighbour next door has more, and he has 29 pearls of this size.”
“That doesnt tell me how many you have” the inspector remarked.
“Well, if I would put all my large pearls in a bag, both black and white, and you would take out two at random, the chances would be exactly 1 in 5 that you would have two black ones.”
“Don’t believe a word he says!” the servant in the shop warned him. “My boss is a notorious LieSpeaker! Our neighbour has 30 pearls of this size, and the chances are exactly 1 in 4 that you would take out 2 white pearls!”

“That makes things clear!” answered inspector Mart. “Thank you!”

How many pearls does the shop owner have? And who is speaking the truth?

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.

When you have solved this puzzle, you can check your solution here

Morozkin problem

Vladimir Arnold in the April 1997 edition of the Notices tells:

The first real mathematical experience I had was when our schoolteacher I. V. Morozkin gave us the following problem: Two old women started at sunrise and each walked at a constant velocity. One went from A to B and the other from B to A. They met at noon and, continuing with no stop, arrived respectively at B at 4 p.m. and at A at 9 p.m. At what time was the sunrise on this day?

This problem can be found at several places on the web, and I assume there is no harm in reproducing it here.
I would like to encourage you to solve the puzzles on your own. It will increase your self confidence, while looking up the answer will lower your self esteem.

When you have solved this puzzle, you can check your solution here

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.

Divide the clock

The illustration shows an old fashioned analog clock.
Usings two straight lines, in how many parts can you divide it so that the digits on all parts have an identical sum?

I found this puzzle on aplusclick.com as a former math olympiad problem.

I would like to encourage you to solve this puzzle on your own. It will increase your self confidence, while looking up the answer will lower your self esteenm.

When you have solved this puzzle, you can check your solution here

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 solutions – 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.

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.

Pattern code – chemistry

1) Graphs
What code goes to the question mark?

You can check your solution>here

 

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?

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?