With basketball season in full speed, this is a great puzzle to startle everyone at the game commercial. It is suggested by our All-Star Puzzle Winner - Kim. Please solve it with me. Kim will determine the puzzle winner.
You are charged with generating the schedule for a single-elimination basketball tournament. There are 247 teams in the tournament. How many games will you need to schedule in order to determine the winning team?
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6 comments:
Since 247 teams are playing and there is one winner - we need to eliminate 246 teams (single elimination). That means that you need 246 games to find the winning team.
Yes, agreed with W. Got to send 246 teams home and the only way they go home is lose. 124 + 62 +31 + 15 + 7 + 3 ... dirty trick with the odd team! Possibly 243 games will do it? Tom
Tom - it is interesting how you contradict yourself by supporting W first and saying that 246 teams should lose playing one game and then offer 243.
It will be 124 + 62 + 31 + 15 + 8 + 4 + 2 +1 = 246
When you have 62 teams playing 31 games, you are left with 31 teams. One team awaits while 30 are playing 15 additional games, eliminating 15 teams and leaving 15 teams plus the one extra for the next round. So, now we have 16 teams. They play 8 games etc.
I was playing with a few different scenarios of game arrangements and was surprise to discover that they all sum to 246.
W. provided a great explanation. Bravo W.!
Yes, that's dead on. Sometimes problems that may initially seem complex can be solved with very simple logic.
246 teams that need to lose, so 246 games.
Excellent puzzle! Kim, thank you so much for sharing it with us.
W's logic is flawless. I actually heard this puzzle as the weekly "puzzler" on NPR's "Car Talk." They reasoned the same way Tom did.
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