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.

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?

Mastermind

Some puzzles are derived from games, such as chess problems, draughts problems or bridge problems. It is rare that a game is built around a puzzle. One such a game is Mastermind, invented by by Mordecai Meirowitz, an Israeli postmaster and telecommunications expert.

For those who don’t know it (are there any such persons in the ‘civilised’ world?), here are the rules. The board is four columns white, and one player sets up a secret combination of colours by selecting 4 pegs from a set of pegs in six colours, as shown in the picture.
The second player has to guess this combination. He may put up his own combination, and the first player will respons with one black peg for every peg with a colour in the correct spot and a white peg for every peg with the colour in the wrong spot. Pegs with a colour which are not in the secret combination are not rewarded at all.

1) 4 colours on 3 spots^*

2) 6 colours on 4 spots^**

There are several variations of the game.
The standard form is one codemaker and one codebreaker. Roles alternate to see who can solve the others pattern is as few guesses as possible. Or in the shortest time.
An alternative is to have several code breakers, not able to see each others guesses, and competing for the fewest number of guesses.
Instead of using colours, one may use digits (0-9), or letters. In the latter case, players are limited to existing words.
More Mastermind puzzles are planned in one of the upcoming e-books.

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

A new puzzle is published every friday, at which time I will also post the solutions to the previous weeks puzzle so you can check yours. I welcome your solution times, but please don’t publish your solutions – that might spoil the fun for others. I also welcome your remarks on the difficulty level, multiple solutions, ambiguities and so on.

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)

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.

Strange calculation?

 

 
IF

8 x 2 = 46416
6 + 3 = 23618
15 : 3 = 513545
9 – 3 = 38127

Then what is :
12 x 4 =?

I am very much interested in your solution times, and you are welcome to make remarks, and discuss alternatives. Pointing out alternative solutions is also welcome, as they point out possible problems in the brain teasers, but please dont mention solutions and leave others the fun to solve them too.

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

Complete the alphabet (3)

1) Complete the alphabet^*

AEFHIKLMNTVWXY
BDGJPRU
COQS

In which row does the letter Z go?

If you solved it, we have the solution to 1

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.

You are welcome to post your solution times, make remarks, and discuss alternatives. Pointing out alternative solutions is also welcome, as they point out possible problems in the brain teasers.

81

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Using four times the number four, create the number 81. You may use the usual mathematical operands.

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

I would like to thank Kees Krol again for coming up with this one.

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.