Category Archives: puzzle

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
大井町
横浜 
-----+
浜松町

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)

Links

  1. online puzzle solver
  2. Mike Keiths site
  3. Sphinx collection
  4. http://bach.istc.kobe-u.ac.jp/puzzle/crypt/out/eg-num.out
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drawings


What’s special about the following sentence?

I am not very adept making awesome drawings.

As usual, you are welcome to report your solution times and comment on the solution, but please do not give away the answer – that may spoil the fun for others. I will publish the solution in one or two weeks after posting the puzzle.

You can check your solution here

Complete the alphabet (3)


Alphabet
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.

Complete the alphabet (2)


Alphabet
1) Complete the alphabet*

ACDGHIMNOPUVWXY
BEFJKLQRST

In which row does the letter Z go?

If you solved it, we have the solution so you can check yours

—-
One of the nice things of wordpress is its detailed visitor stats.
This blog had 6900 views in 2012.

The visitors have come from (in from most to fewer, only countries > 5 views represented:

United States India United Kingdom Netherlands Canada Australia
Ireland, Philippines Singapore Belgium Turkey Pakistan Germany Romania
Saudi Arabia France Spain Brazil Jordan Korea, Malaysia Hong Kong Greece
Poland Denmark New Zealand Italy Indonesia United Arab Emirates Norway
South Africa Sweden Taiwan Switzerland Mexico Algeria Israel Austria
Lebanon Finland Portugal Qatar Iceland Iraq Hungary Kuwait Jamaica
Ukraine Nigeria Russian Federation Egypt Serbia Bangladesh Japan
Thailand Belize Slovakia Viet Nam Nepal Argentina Latvia Kenya Estonia Armenia

There were 38 new posts, brining the total up to 52. 127 new pictures were uploaded.
The busiest day of the year was December 17th with 97 views.

The most popular posts date back to 2011, all types of river crossing puzzles.
Oh, and the most poopular page was the page with the solutions.

Perfect logicians


Pirate smiley1) The five pirates**
Five pirates have 100 gold pieces. They are all perfect logicians, greedy , and blood thirsty.

They have a strict order of seniority, and the most senior pirate makes a proposal how to divide the 100 gold pieces among them. The pirates vote on the proposal. If the proposal is accepted (more votes for than against, or the number of votes are equally divided), the 100 gold pieces are divides as per proposal.
The gold pieces can not be divided into fractions, and all pirates are know that the others are logical too. Moreover, they don’t trust each other, so any deals among the pirates are not possible.

If the proposal is rejected (at least as many votes against as in favour of the proposal), the pirate who made the proposal is killed and the pirate who is next in order of seniority makes a proposal. That can continue till there is just one pirate left.

When casting his vote, the priorities of each pirate are:
I) Stay alive himself
II) Get as much gold as possible
III) Kill off other pirates
All 5 pirates are perfect logicians, and immediately sees the result of any proposal and will, with the a fore mentioned priorities in mind, cast his vote.

Which proposal should the most senior pirate make?

2) Five pirates again**
This puzzle is the same as above, with two changes:
a) If the votes on a proposal are equally divided, the proposal is rejected.

3) How many pirates?**
How many pirates can take part in the division of 100 gold pieces, with the rules from puzzle 1, with the first one still surviving? And how does the pattern develop with an ever increasing number of pirates?

There is of course no intrinsic reason why the persons in this puzzle should be pirates. They could easily well be immigrants from Pluto on Mars, or be hula-hoop girls on a remote pacific island. I have retained the pirates as figures because people are most likely to search for this word when trying to study this puzzle.

If you solved it, we have the solution to 1

If you solved it, we have the solution to 2

If you solved it, we have the solution to 3

Gratte ciel


Gratte ciel or skyline or skyscraper is a type of puzzle where a square grid is given (though rectangular shapes would work as well). Every square in the grid has a skyscraper of 10, 20, 30 or 40 high in a 4×4 grid. The number of different skyscrapers that can be seen from an edge is given along that edge.

For example, if in a row the heights of the skyscraper are 20, 10, 30 and 40 respectively, 3 skyscrapers are visible from the left, as the 10 is hidden behind the 20. Only 1 is visible from the right: the one with a height of 40.

Like many modern puzzles, I don’t know where it was invented first. I have seen it around for several years now.

This one should be a nice and easy introduction:
1) 4×4*
4x4

2) 5×5**
5x5

3) 5×5**
5x5

If you solved it, we have the solution to 1, solution to 2 for you.

For the third puzzle, we have some Hints

Sometimes empty spots are introduced, called parks. they can be regarded as skyscrapers of height 0. It really doesn’t change the puzzle, by simply adding 10 to every height it transforms into the standard form.