Ages

Ages^**/*****

Ages^**/*****
A man is 25 years old and his wife 23. He noticed that the sum of their ages (25+23=48) is exactly 4 times the sum of the digits of their ages. (2+5+2+3=12).

When will the sum of their ages be exactly 8 times the sum of the digits of their ages? And when will it be 9 times the sum of the digits?

You can check your solutions here

New puzzles are published at least twice a month on Friday. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.

Find a 4 digit number

Number^**/*****
Find a four digit number abcd such that
– abcd is a prime number,
– a+b+c+d = 10,
– the sum of the digits of ab*cd equals 7.

You can check your solutions here.

New puzzles are published at least twice a month on Friday. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.

On the first day of Christmas…

1) On the first day of Christmas^**/*****
On the first day of Christmas, my true love brought to me:
On the first day of Christmas
My true love gave to me
A partridge in a pear tree

On the second day of Christmas
My true love gave to me
Two turtle doves
And a partridge in a pear tree

Thus go the first two couplets of a traditional Christmas song. Question is:
Haw many things did my true love give me over these 12 days? (counting the partridge in the pear tree as one item)

You can check your solutions here

2) On the second day of Christmas^**/*****
Yeah, in puzzle 1 above you had the classical song. But in puzzle land, everything is different.
In puzzle land, on the second day of Christmas my true love brought me this puzzle:

“This puzzle consists of @ letters”

With what number (spelled out, of course) should @ be replaced to be true?

You can check your solutions here

3) On the third day of Christmas^**/*****
On the third day of Christmas, my true love brought to me this puzzle:

“This puzzle consists of @ vowels and # consonants”

Again, by which numbers, spelled out, should @ and # be replaced to yield a true sentence? Please note that “y” is counted as a vowel.

You can check your solutions here

New puzzles are published at least twice a month on Friday. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to three stars.

The anchor puzzles

Starting in 1890, the German firm Richter produced a series of Tangram puzzles which were widely distributed during the First World War, or The Great War as it was then called, as a pastime for the troops in the trenches. With the pieces consisting of stone, they could survive in the horrible environment. They were used by both German and British troops.
The puzzles came together with sheets with exercises, which have been compiled by Jerry Slocum, one of the worlds greatest puzzle collectors. He published the exercises in a book, which you can order here. The firm stated that some of the problems have been contributed by the troops.
The anchor factories are now owned by Goki.

I recently purchased a series of anchor stone puzzles at internet-toys.com (Another supplier is http://www.padilly.com/brainteasers.html). Their delivery was speedy and accurate, and they have low prices. The puzzles arrived within a few days, though of course I can not vouch for delivery times in the rest of the world.
The puzzles are still made of stone, and below you find pictures of the once I obtained. Currently they do not offer the full range. The ones they do offer are in bright green, yellow, blue and red. The back of the cardboard boxes do mention Anker Steinbaukasten GmbH. There are no names of the individual cardboard boxes. Some of the boxes carry a number of puzzles on the inside of the box, some don’t. None had a solution, and the drawings on the cover do not match the inside arrangement of the pieces. This, the boxes state, is on purpose: no clue is given away. You did want to puzzle, did you?

There are 3 historical puzzles, which in “Puzzles old and new” by Jack Boterman and Jerry Slocums are called Zornbrecher, Wunderei / Ei des Columbus (I don’t see much difference between these two in their book) Herzratsel and Kreisratsel. These are the ones that come with the 10 exercises on the inside of the box.

The big surprise for me are the other puzzles: The do not seem to match any of the traditional Anker puzzles. At internet toys they are labelled maan, dennenboom, ster en kruis in Dutch, which translates into English as moon, pine, star, and cross.

Expect some exercises in the future with these new puzzles, though the usage of non rectangular shapes may cause some troubles in this endeavor. For the moment, here are the puzzles:

New puzzles are published at least twice a month on Fridays. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to three stars.

Japanese tangram

A few weeks ago I wrote about a Japanese Tangram from 1742, pre-dating the well known Chinese Tangram, and gave some classical figures with the 7 pieces. This week I’d like to present some figures wit the theme: In and around the water.

Again I’d like to thank my wife Jos and our daughter Margreet for coming up with these figures.

You can check your solutions here

A new puzzle is published every Friday. Solutions are published after one or more weeks. You are welcome to discuss the puzzles, their difficulty level, originality and much more.

3 3’s

Use 3 3’s to make exactly 20.
Hint: USA inhabitants have it easier.

You can check your solutions here

A new puzzle is published every Friday.

Squares

It is trivial to divide a square into 4 squares:

Divide a square into:
a) 6 squares
b) 7 squares
c) 8 squares (2 ways)
d) 9 squares (2 ways)
e) 10 squares (2 ways)
f) 11 squares
The squares should not overlap.

A new puzzle is posted every friday. You are welcome to comment on the puzzles. Solutions are added at the bottom of a puzzle after one or more weeks.

You can check your solutions here

The ingenious pieces of Sei Shonagon

Tangram is one of the best known puzzles in the world, and went through at least two fads: one in the early nineteenth century, and once more when American puzzlist Sam Loydd published a booklet about it. The oldest known tangram dates back to about 1800.

In 1742, a little book about a Japanese seven-piece puzzle was published under the pseudonym Ganreiken. The real name of the author is unknown. The title was “Sei Shonagon Chie-no-ita”, or the ingenious pieces of Sei Shonagon. Sei Shonagon was a court lady who lived approximately 966 – 1017. There is no clear reason why Ganreiken named his 32 page booklet after her. The booklet has 42 patterns with answers, but the shapes are inaccurate. A copy of the booklet has been distributed at one of the International Puzzle Parties, but as I’m not in contact with anyone in higher puzzle circles I don’t have access to it. A year later Ganreiken published another book with more exercises. In about 1780, Takahiro Nakada wrote a manuscript entitled “Narabemono 110 (110 Patterns of an Arrangement Pattern),” and Edo Chie-kata (Ingenious Patterns in Edo) was published in 1837. Alas I was unable to find these figures on the internet.

There are surprisingly few publications in the west about this puzzle. Jerry Slocum devotes half a page of it in his book “The history of Chinese Tangram”, and Jerry Slocumn and Jack Botermans describe it in their “Zelf puzzels maken en oplossen”.

The Sei Shonagon consists of 7 pieces, like Chinese Tangram, which make up a square. Unlike Tangram, they can be fitted together to make up a square in two different ways.



I will leave the other square as an exercise for you.

They can also form a square with a whole in the middle:



The figure with the hole in the middle is one of the original puzzles.

Where the Chinese tangram has 13 convex shapes, Philip Moutou showed that Chie no-ita has 16 possible convex shapes. In geometry, a shape is called convex if any two points of the figure can be connected by a straight line which is entirely within the figure. I intend to publish about them in a subsequent post.

Presented here are 28 of the original problems.

You can check your solutions here

A new puzzle is published every Friday. Solutions are published after one or more weeks. You are welcome to discuss the puzzles, their difficulty level, originality and much more.

The hiker, the bicycle and the moped

Alexandra, Bernadette and Cindy all want to go from A to B. The distance is 60 km. (If you prefer miles, simply read miles instead of kilometers in this puzzle.)

They have a bicycle and a moped. Both are without backseat, so only one person can use them at any time.
A hiker walks 5 km/hour.
A Cyclist goes 10 km/hour.
The moped rider makes 20 km/hour.

A hiker would take 60/5=12 hours.
A cyclist would take 60/10=6 hours
The moped rider would take 60/20= 3 hours.
Together that is 12+6+3=21 hours, or 7 hours average.

Is there a way, by alternating transport means, that the three people all can make it in 7 hours?

If you are stuck, one possible solutions is given here. Be aware that more solutions are possible.

This puzzle is based on a similar problem in Pythagoras, issue 1 1967/1968. The distance and the speeds have been changed.

It is easy to see simplify this problem to 2 persons, A and B. The solutions become pretty trivial. But how about expanding the puzzle to 4 people, or 5, or even to n people?

A new puzzle is published every friday. You are welcome to comment on the puzzles. Solutions are usually added after one or more weeks.

Chaos checks

In september last year, I wrote about ‘Vinken’ or ‘Checks’, a Sanders puzzles publication. My main comment was that it was a nice puzzle variation, but that the puzzles were slightly too easy. Sanders puzzels corrected this in later issues.

I did come up wit a slight variation, though the puzzle I designed didn’t make the puzzle difficult enough for my tast. Anyway, I’d like to present this variation to the world.

The rules are simple:
– every row and column, and every 9 sized area, contains 3 checks.
– the checkmarks are never adjacent horizontally or vertically. They may be adjacent diagonally.
– some checkmarks have been pre-filled, as well as some empty squares.

Here are three examples.
puzzle 1^*
As you can see some checks and some empty positions have been given. You hve to derive the position of the remaining checks.

puzzle 2^*
This time only some empty positions have been given as clues.

puzzle 3^**
Again only some empty positions have been given as clues.

You can check your solutions here

A new puzzle is published every Friday.