Problem Description : with 36 cars and 6 runways without a timer, the fastest 3 cars can be screened at least several times in a few races?
Scenario 1: cannot be marked
- The 36 cars were divided into 6 groups, each group of 6 vehicles, each group to compete, leaving behind each group of the top 3. 18 More cars (6 times)
- The 18 cars were divided into 3 groups, each group of 6 vehicles, each group to compete, leaving behind each group of the top 3. 9 More cars (3 times)
- Choose 6 from 9 cars for one game and leave the top 3. 3 cars left and 3 cars not competing, and 6 cars (1 times)
- Last 6 car races selected Top 3 (1 times)
Total 6+3+1+1=11 times
Scenario 2: Can be marked
Method 1 (8 times)
- The 36 cars were divided into 6 groups, each group of 6 vehicles, each group to compete, leaving behind each group of the first 3, marked. Get A1, A2, A3 、...、 F1, F2, F3 a total of 18 vehicles (6 times)
- Choose the 1th place in the last match for each group to play and get the top 3. A1, B1, C1, D1, E1, F1---> D1, A1, E1 (assuming these three, does not affect the results) (1 times)
- The 1th place in the last game, D1, was the final 1th place. Select D2, D3, A1, A2, E1 (2, 3 in the 1th Group, 1 or 2 in the 2nd place, and 1th in the group 3rd) a total of 5 cars for a race, the top 2, the two cars and D1 make up the final result (1 times)
Total 6+1+1=8 times
Method 2 (7-10 times)
- Choose 6 cars for a race, get the top 3 marks for S1, S2, S3 (1 times)
- The remaining 30 vehicles are divided into 6 groups, each with 5 vehicles. Each group of 5 cars and S3 to play. If the S3 in each group is the fastest, end (6 times)
- Otherwise, in the worst case, from the last 6 groups of 3 A1, A2, A3 、...、 F1, F2, F3 a total of 18 vehicles Select the Top 3 (2 times, with Method 1)
- The last 3 matches with S1, S2, S3 and the final result (1 times)
Total 1+6=7 (best), 1+6+2+1=10 times (worst)
Method 3 (10 times)
- 36 cars divided into 6 groups, Each group of 6 vehicles, each group to compete, leaving the top 3 per group, labeled A1, A2, A3 、...、 F1, F2, F3 a total of 18 vehicles (6 times)
- first place of each group race A1, B1, C1 , D1, E1, F1 left Top 3 B1, A1, F1 (1 times)
- first match each group's second place to play a race A2, B2, C2, D2, E2, F2 leave top 2 A2, E2 (1 times)
- third place in each group of the first match A3, B3, C3, D3, E3, F3 leave 1th place B3 (1 times)
- b1, A1, F1, A2, E2, B3 6 cars, 1 races, Get the final result (1 times)
Total 6+1+1+1+1=10 times
So the quickest way is 7 times, the most stable and fast way is 8 times.
deformation 1: 25 horses, 5 runways, pick the fastest 5 horses
Have marked
- 25 horses were divided into 5 groups, each group of 5 horses, each race, labeled A1, A2, A3, A4, A5 、...、 E1, E2, E3, E4, E5 (5 times)
- The 1th place in each group played the 1th place of the A1, B1, C1, D1 and E1 as the final first place, assuming B1 (1 times, 1 horses were selected)
- Each group of the current 1th place for the match A1, B2, C1, D1, E1 get 1th place as the final second (1 times, 2 horses selected)
- And so on, you can pick one of the fastest horses in every game.
Total 5+1+1+1+1+1=10 times
Variant 2: There are 38 cows, 6 tracks, and the fastest 3 cows run.
No tag
Method 1 (13 times)
- The 36 cows were divided into 6 groups, respectively, leaving the top 3, a total of 18 cows, and a total of 20 heads (6 times) without participating in the competition.
- 20 cows were divided into 4 groups, 5 cows per group, 3 in total, 12 cows (4 times)
- 12 cows were divided into 2 groups, 6 cows per group, 3 in total, 6 cows (2 times)
- The remaining 6 cows race, get the final result (1 times)
Total 6+4+2+1=13 times
Method 2 (11 times)
- Randomly pick out 2 cows from 38 cows and not compete (0 times)
- Choose the fastest 3 cows to run from the remaining 36 cows (11 times, same situation 1)
- Pick out 2 cows and select 3 cow races to get the final result (1 times)
Total 11+1=12 times
Have marked
- Randomly pick out 2 cows from 38 cows and not compete (0 times)
- Choose the fastest 3 cows to run from the remaining 36 cows (8 times, the same condition as 2 Method 1)
- Final match once, get results (1 times)
Total 8+1=9 times
36 Cars and 6 tracks, screened for the fastest 3 cars
