thnik again!

Tennis has its Wimbledon, soccer its World Cup, and chess its Olympiade. It took place in Dresden, Germany, recently with about 150 four teams in the Men section.

Every team was ranked before the tournament and so was every player. How likely is it that a better ranked team beats a lower ranked team? How likely is it that a better ranked player beats a lower ranked player?

In my opinion the answer will say something of how good the ranking system is.

The same question can, of course, be asked for ranked tennis players, ranked national soccer teams, etc.

Have anyone studied this problem? I am all ears.

In the chess olympiade round 8 these were some of the results:

In four of the six team matches the better ranked team won and in one case the worst ranked team won. In ten of the 24 individual games the better ranked player won and in four cases the worst ranked player won. It would be nice if I could find tons of data of this sort ready to analyse.

Go here and try to solve this problem interactively. If you don’t know the game of Go, it is about time. It is over 4000 years old. Where have you been?

1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321

1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111 

9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888

Amazing or expected?

Source: Desi Baba’s Get The Knowledge Spread The Knowledge.

I base my fashion taste on what doesn’t itch. - Gilda Radner

Easy question: Who recorded ‘Run for your life’ and when?

More difficult question: Who was Richard Reti and how can Black whose turn it is win in the position below? Black moves down the board.

The man who reads nothing at all is better educated than the man who reads nothing but newspapers. - Thomas Jefferson

Last night I got an angry phone call. The conversation is not fit for print, but the complaint was that the problems in this blog are generally far too difficult.

To rectify the situation, here comes today’s no-brainer.

Bingo cards are flat pieces of cardboard or non-reusable paper which contain 25 squares arranged in five vertical columns and five horizontal rows; Dual dab, or “double-action” cards have two numbers in each square. Each space in the grid contains a number, except for the center square, which is considered filled. The highest number used is 75. The letters B, I, N, G, O are pre-printed above the five vertical columns, with one letter appearing above each column. The center space is marked “Free”. The printed numbers on the card correspond to the following arrangement: 1 to 15 in the B column; 16 to 30 in the I column; 31 to 45 in the N column; 46 to 60 in the G column and 61 to 75 in the O column. - From Wikipedia.

How many  possible arrangements exist of the numbers on a bingo card?

Beware of the man who works hard to learn something, learns it, and finds himself no wiser than before… He is full of murderous resentment of people who are ignorant without having come by their ignorance the hard way. - Kurt Vonnegut

Several months after Bingo hit the market, Lowe was approached by a priest from Wilkes-Barre, Pennsylvania. The Father had a problem in his parish. A fast thinking parishoner had come up with the idea of using Bingo as a way to get the church out of its financial troubles. The priest had put the scheme into operation after having bought several sets of Lowe’s $2.00 Bingo game. However, problems developed immediately when it was found that each game produced half a dozen or more winners. - History of Bingo

Each Bingo card has five columns. In the first column appears five numbers from 1 to 15, in the second five from 16 to 30, in the third four from 31 to 45, and in the fourth and fifth five numbers from 46 to 60 and 61 to 75 respectively.

If a winner is the one who first gets a row, column, or main diagonal filled (the center cell is filled in from the start), how many cards can be made that always will create only one winner?

If you find that problem too hard, try instead to answer it for a 3×3 board that uses numbers from 1 to 27 with a free square in the center.

Failing that, try a 1×1 board with numbers from 1 to 3 and a free square in the center.

Why does the Air Force need expensive new bombers? Have the people we’ve been bombing over the years been complaining? - George Wallace