# 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 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.

# My colleague and his daughter

This week a colleague brought some cake for his birthday. He didnt want to tell his age, but he did reveal that he and his daughter together were 46 years old, and that in eleven years he would be thrice as old as his daughter.
What are their ages?

You can check your solutions here

# Coded germs

One of the type of puzzles taht has become a trademark of this blog are ‘coded patterns’

Which code goes to the question marks?

You can check your solution here

You are welcome to remark on the puzzle: its wording, style, level of difficulty. I love to read your solution times. Please do not spoil the fun for others by listing the solution. Solutions will be posted after one or more weeks.

# The spy and the sentry

A spy wanted to enter a castle, but this castle was guarded by a sentry. Only those who knew the password, were allowed to enter. The spy hid himself in the bushes near the guardhouse of the sentry, so that he could overhear the password.
The baker approached, and the sentry called:
‘If I say 12, what do you reply?’
‘6’
‘You may pass.’
The smith approached, and the sentry called:
‘If I say 6, what do you reply?’
‘3’
‘You may pass.’
The spy concluded: ‘I know enough’
With a long detour he went back, disguised himself as a grocer and approached the sentry. The sentry called:
‘If I say 4, what do you reply?’
‘2’
The spy was taken prisoner.
What should he have replied?

I would like to thank our daughter Margreet for passing on this nice problem, which she heard from Professor Jochem Thijs. Alas he did not reply to my question if he invented this puzzle or not. If he is not the inventor, and someone knows the original source, I would be grateful.

You can check your solution here

You are welcome to remark on the puzzle: its wording, style, level of difficulty. I love to read your solution times. Please do not spoil the fun for others by listing the solution.

# Problems = Puzzles?

In the following puzzle, every letter stands for exactly 1 digit.

You can check your solutions here

# Digital matchsticks (4)

Move 2 matchsticks to get a correct equation:

You can check your solutions here

# Which number does not belong in the following series? (2)

Which one of the numbers does not belong in the following series?
3, 4, 8, 9, 10, 18, 19, 38

You can check your solutions here

# Cryptarithms

Cryptarithms, alphametics, verbalarithmetic are some of the names of a type of puzzle, where two, three or more words are given, and each letter must be replaced by a single digit. The most well known of this is:
1) Dudeneys classic**

``` SEND
MORE
-----+
MONEY
```

Replace each letter with exactly 1 digit and make it a correct addition. The example above is from Henry Dudeney.

(Solution: 10)

Verbal arithmetic puzzles are quite old and their inventor is not known. An example in The American Agriculturist[2] of 1864 makes the popular notion that it was invented by Sam Loyd unlikely. The name crypt-arithmetic was coined by puzzlist Minos (pseudonym of Simon Vatriquant) in the May 1931 issue of Sphinx, a Belgian magazine of recreational mathematics. In the 1955, J. A. H. Hunter introduced the word “alphametic” to designate cryptarithms, such as Dudeney’s, whose letters form meaningful words or phrases.

There are several types of cryptarithms. One of them is them is the double true. This type of cryptarithm shows an addition that is true in words, but can also be deciphered as a cryparithm. This puzzle comes from N. Tamura, who wrote a program to search for puzzles with a unique solution.
2) DOUBLE TRUE:**

``` THREE
FIVE
FIVE
SEVEN
TEN
------+
THIRTY
```

(Solution: 30)

3) Math formulas* are another subcategory.
This one was first published in Sphinx magazine, and republished by Jorge A C B Soares. He mentions M. Van Esbroeck as the author, and january 1933 as the date of first publication.

``` A B C = C4
B C A = D4
```

(Solution: 40)

Cryptarithms are of course language dependent. However, they are not limited to the English language. The booklet CIJFERWERK (digit work), written by J. van der Horst, published by Born periodieken, date unknown, isbn 8 710838 100910, has some 200 dutch cryptarithms. In Germany they are called “Kryptogramm”, in French “Cryptarithme”, or d’alphamétique. I see articles on them in the Japanese wikipedia, where they give the following example:
4) Japanese*

```　大宮
×大宮

-----+

```

Please forgive me that my Japanese is insufficient to discover the author.

(Solution: 70)

5) List**
Lists are another subcategory of this puzzle type. Lists are composed of a number of items in category, followed by the name of the category, which equals to the sum of the items. In a good list items are unique, taht is, they appear only once.

Here is a non unique list, that is a list with items that appear more than once:

```APPLE
PEAR
DATE
APPLE
PEAR
DATE
APPLE
PEAR
DATE
APPLE
PEAR
DATE
-----+
FRUIT
```

(Solution: 50)