eleven children enter the chess competition at school .each player plays one match against every other player .
haw many matches are there in total ?
2007-07-07 09:50:21 · 10 answers · asked by mark100414 1 in Science & Mathematics ➔ Mathematics
55.
Each player would tell you that they played 10 other players, so if you tallied up the games by asking each player, you'd get 11 (players) * 10 (games-per-player), for 110.
However, that counts each game twice. Player A would count his match against Player B in his total, but Player B would report that same match in his own total.
You have to divide by two, to compensate for that double-counting: 11*10/2 = 55.
2007-07-07 09:52:14 · answer #1 · answered by McFate 7 · 3⤊ 0⤋
How I would work this out:
Player 1 plays all other 10 players = 10 matches
Player 2 plays all other players except player 1, as already played him = 9 matches
Player 3 plays everyone except 1 and 2 (who he's already played) = 8 matches
etc will go all the way down to 1.
So the total number of matches will be 10+9+8+7+6+5+4+3+2+1=55.
If you had a similar problem with e.g 501 players, doing that addition sum would take a long time! A quick way to add the sequence is to put the numbers in pairs:
10+1=11
9+2=11
8+3=11 etc.
As there are 10 numbers, there must be 5 pairs. So we have 5*11=55.
2007-07-09 03:36:04 · answer #2 · answered by Steve-Bob 4 · 0⤊ 0⤋
10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 55
2007-07-11 06:12:22 · answer #3 · answered by Jun Agruda 7 · 2⤊ 0⤋
Each of the 11 players has to play against the other 10, giving 11 * 10 matches. However, that includes A playing B and B playing A, and so it needs to be halved:
11 * 10 / 2 = 55.
2007-07-07 09:56:19 · answer #4 · answered by Anonymous · 0⤊ 0⤋
Each person will have played against the ten other players, since there are 11 players, 11*10 is 110. Now since two people are in one match, 110/2=55 so there are 55 matches in total.
2007-07-08 03:11:54 · answer #5 · answered by Anonymous · 0⤊ 1⤋
another way to solve it would be like this: 10+9+8+7+6+5+4+3+2+1=55 :)
2007-07-07 10:27:06 · answer #6 · answered by Yaasi 3 · 0⤊ 0⤋
11 children x 10 matches each. But then you must divide by two if you want each pair to only have one mach. Therefore, your answer would be 55 matches.
2007-07-07 10:18:54 · answer #7 · answered by Anonymous · 0⤊ 0⤋
Well everyone's beaten me to this one and everyone's correct!
For the record, the formula for this type of question is:
n(n-1)/2 Where n is the number of players.
2007-07-07 10:54:31 · answer #8 · answered by brainyandy 6 · 0⤊ 0⤋
Hi
I am only 9 and i can tell you the answer it is 55. Good luck with the rest of your homework, and have a nice summer school holiday.
2007-07-07 10:05:28 · answer #9 · answered by cj 4 · 1⤊ 0⤋
132
2007-07-11 05:32:51 · answer #10 · answered by maclaren 4 · 0⤊ 0⤋