Wednesday, September 5, 2007

a geometry question - 4


AB = BC = CA
BD = 8
CD = 7
AD = 5
Find the BDA angle.

Answer:
120°
(The solution method other than a "brute force" method eludes me. I prepared this question 12 years ago, and I assume there was an easier method. If anybody knows such a method, let me know at karakusk at yahoo dot com.)

Tuesday, September 4, 2007

a geometry question - 3


BD =DC and AE = EC given.

Find the unknown angle.

Answer:
20°

Monday, September 3, 2007

a geometry question - 2


Find the unknown angle.

Answer:
70°

a geometry question - 1


Find the unknown angle.

Answer:
130°

Sunday, August 19, 2007

a "retro" chess problem


white plays and mates in two.

solution and explanation:

1. fxe6 e.p. f5 2. Bxf5 mate.

the only last possible move of black can be e7-e5. all 16 white pieces are on board so d6xe5 is impossible. e6-e5 is impossible as a black pawn at e6 would have given check. other possible last moves are discarded in a similar way.

the position is legal as far as i can tell. white pawn structure indicates minimum 4 captures and this is possible as there are 9 black pieces on the board.




knights cannot triangulate


white plays and draws.

solution:

1. Kg2 Nb6 2. Kg1 Nd5 3. Kg2 Ne3 4. Kg1 draw...

Thursday, July 26, 2007

a bilingual crossword puzzle

the idea: creating a crossword puzzle for which the clues can be asked both in Turkish and in English. for this purpose,
- homonym words or names that have different meanings in the two languages (such as "fare", the word for "mouse" in Turkish),
- or words or names that denote the same thing that is common to the cultures related to both languages (e.g. Paris)
can be used.

the method: first a list of words of 4 or more letters (words of 2 and 3 letters should be easy to spot and numerous) that can go into this puzzle will be listed. the second step is preparing the puzzle using this list.

the issues: the two cultures have different crossword styles. while in english crosswords the black squares tend to be more structured, the Turkish puzzles care more about how many of those black square touch each other and in what ways. the puzzle i am planning to prepare will be more akin to the Turkish style, and it will be 10 x 10 (English puzzles tend to be bigger). i am not expecting a high quality in the sense of the black square number and structure.

there is also differences in the way the clues are asked: the English clues tend to be more riddle-like / indirect where the Turkish counterparts tend to be more encyclopedic / direct. however this should not be a problem since the focus here is on more the puzzle itself as opposed the clues.

one last non-issue is that we will assume the Turkish letter İ/i corresponds to the English letter I/i following the convention in Turkish crosswords.

the "common words" list: (not exhaustive)
4 letters: adam, baba, bale, bank, bask, beta, bile, bone, bora, cart, fare, file, fire, gala, gong, grad, gram, halt, iman, iran, judo, kilo, king, kurt, lake, lame, lice, lime, lira, mail, mali, mama, mana, mark, mars, mask, maya, mayo, mine, nail, name, nice, nine, papa, park, peru, pike, polo, post, rant, ring, risk, said, sake, salt, side, silo, sine, site, star, sumo, tank, test, tire, trap, yare, yoga
5 letters: abide, amber, argon, asker, aslan, atlas, belli, bilge, burma, delta, dingo, durum, haiti, ideal, joker, karma, kazan, kenya, koala, latin, litre, malta, mason, metal, metre, model, moral, moron, motel, ninja, organ, panda, paris, pasta, pepsi, peter, pizza, poker, robot, salsa, samba, seven, sudan, tamer, tokyo, topaz, totem, yemen,
6 letters: alaska, artist, banker, broker, brunei, defile, define, demode, fiesta, filler, halter, hangar, hilton, karate, market, metres, millet, panama, pardon, pastel, petrol, postal, siesta, sprint, tanker, uganda,
7 letters: amalgam, baklava, bermuda, damping, holding, matador, mineral, moldova, uruguay, vietnam,
8 letters: festival, hong kong, idealist, king kong, pakistan, paraguay, terminal,
9 letters: guatemala, kilometre, milimetre, orangutan,
10 letters: militarist, minimalist


resulting puzzle:




















notes: i do not want to go thru all the clues as their english / turkish explanations can be found in the dictionaries. it still might be helpful to give some explanations (word: turkish / english)
lo: ks. İsveç İşçi Sendikaları Konfederasyonu / ...
il: ... / 49 with roman numerals
okur: ... / "mehmet ..." (NBA player from Turkey)
ana: ... / a collection of miscellaneous information about a particular subject
torun: ... / "nowhere ..." van damme movie (2 words)
ud: ... / short. university of dayton
ma: eski dilde su / ...
abel: "niels ..." (matematikçi) / ...
eat: ks. eski anadolu türkçesi /...
ran: nazım hikmet'in soyadı / ...

conclusions: the puzzle didn't end up too much of a "high quality" puzzle, as the words that can be used are quite limited. many acronyms and proper names are used (this might be a bit excessive for a regular daily crossword). all in all, i have shown that a crossword puzzle that is meaningful in two languages is possible.

Tuesday, July 17, 2007

strict locality

strict locality: the effect of any object or event is limited to a certain scope within the universe.

Thursday, July 5, 2007

16 ways 2 objects can be demanded (a logical exercise)

4 ways 2 objects can exist:

  1. 01 : B
  2. 10: A
  3. 11: A and B
  4. 00: none

16 ways 2 objects can be demanded:

  1. 0001 : neither A nor B
  2. 0010 : A and B
  3. 0011 : either A and B together or neither of the two
  4. 0100 : B by himself
  5. 0101 : not A
  6. 0110 : B
  7. 0111 : not A by himself
  8. 1000 : A by himself
  9. 1001 : not B
  10. 1010 : A
  11. 1011 : not B by himself
  12. 1100 : exactly one of the two
  13. 1101 : at most one of the two
  14. 1110 : at least one of the two
  15. 1111 : do not care
  16. 0000 : null (no comment case)

Key: (only A) or (only B) or (A and B) or (none)
eg: 0101 means B by himself or none => not A