Friday, May 09, 2008

I don't want to grow up

Last weekend, I saw an advertisement again about a garage sale somewhere close to my house. I never thought about going, but figured why not and just check out what was there. I didn't expect to buy anything but when I was there, I found Lots and lots of toys for sale.

Like a little boy in toys 'R Us, I was counting my money of what things I could buy. While in my head, there was this Toys 'R Us Jingle playing.....
"I don't want to grow up, I'm a Toys' R Us kid
There's a million toys at Toys 'R Us that I can play with! From bikes, to trains, to video games, It's the biggest toy store there is! Gee whiz! I don't want to grow, cuz baby if I did, I wouldn't be a Toys 'R Us kid!"

Anyway, I got myself a foosball table, a wall climbing harness, a Pirates of The Caribbean chess set, a set of dominoes pieces and a bunch of gambling chips. I don't know why I got them, not like I got anyone to play it with, but ever since I was a kid, I always wanted a foosball table, but it was always too expensive. But this time, it was selling for only 25USD. So I got it anyways, as a decoration in my gym/play room.

Monday, May 05, 2008

Who Killed the Duke of Densmore?

The idea of using interval graphs in detective stories was exploited in depth by Claude Berge in his novelette Que a tuZ le Duc de Densmore? (Who killed the Duke of Densmore?, Bibliotheque Oulipienne No.67). The story presented ideas of using Graph Theories to help solve realistic problems. However, getting this as an assignment can be far from realistic of getting a good grade. So anybody knows who killed Duke of Densmore, please tell me. I know the answer, but i can't solve it using Interval graphs or the academician style of explaining it in interval graphs. The question is as below:

The Duke of Densmore is found dead in the explosion of its castle on the Isle of White. The murder was committed with a bomb placed carefully in the labyrinth of the castle, which would require a long preparation in hiding in the mazes of the labyrinth. During his last years, the Duke had received eight visitors at his castle; each of them was brought first to the island and then back to the mainland by a motor boat. None of them recalls the precise dates or duration of her stay on the island, but each remembers with certainty whom else she had met on the Isle of White:

-- Ann saw Betty, Cynthia, Emily, Felicia and Georgia
-- Betty saw Ann, Cynthia and Helen
-- Cynthia saw Ann, Betty, Diana, Emily and Helen
-- Diana saw Cynthia and Emily
-- Emily saw Ann, Cynthia, Diana and Felicia
-- Felicia saw Ann and Emily
-- Georgia saw Ann and Helen
-- Helen saw Betty, Cynthia and Georgia

The testimony of each woman is comfirmed by the others and collusion between any two is out of question.

If you are a detective like Sherlock Holmes, and also happens to be a Graph Theory enthusiast, how do you find the killer. The killer must have stayed in the labyrinth once, or perhaps several times in order to prepare for her evil plan. Also, none of the suspects are giving false testimony, cause the Sailor who transported the suspects confirmed their testimony. However, the possibility of two people were at the same place and at the same time, but not see each other is highly probable. Any ideas?

There are a couple of ways to answer this question, you either need to be good at graph theory or have exceptional googling skills. I tried Googling, but can't find the exact solution I wanted.