Eight people A, B, C, D, E, F, G, and H live on eight different floors of a building numbered from 1 (lowest) to 8 (highest). Each person ran a different distance in a marathon: 2300 m, 3800 m, 5000 m, 6400 m, 7200 m, 6300 m, 9100 m, and 10000 m. Given the following clues:

- The person who ran 5000 m lives on an even-numbered floor above floor 5.
- Exactly three people live between the person who ran 5000 m and G.
- The person who ran 9100 m lives immediately above E.
- Exactly two people live between the person who ran 9100 m and A.
- A does not live on the topmost floor.
- The total distance run by people living on floors 3 and 6 is 11400 m.
- The person who ran 6300 m lives immediately above the person who ran 3800 m.
- Neither E nor A ran 6300 m.
- Exactly two people live between B and the person who ran 6300 m.
- The person living immediately below D ran a distance more than B but not the highest distance.
- No one lives between H and the person who ran 7200 m.
- E did not run 7200 m.
- The person who ran 10000 m lives immediately above D.
- C and G together ran 16300 m, with C running more than G.

If M ran 2000 m more than B, for how many meters did M run?

Question

Eight people A, B, C, D, E, F, G, and H live on eight different floors of a building numbered from 1 (lowest) to 8 (highest). Each person ran a different distance in a marathon: 2300 m, 3800 m, 5000 m, 6400 m, 7200 m, 6300 m, 9100 m, and 10000 m. Given the following clues:

- The person who ran 5000 m lives on an even-numbered floor above floor 5.
- Exactly three people live between the person who ran 5000 m and G.
- The person who ran 9100 m lives immediately above E.
- Exactly two people live between the person who ran 9100 m and A.
- A does not live on the topmost floor.
- The total distance run by people living on floors 3 and 6 is 11400 m.
- The person who ran 6300 m lives immediately above the person who ran 3800 m.
- Neither E nor A ran 6300 m.
- Exactly two people live between B and the person who ran 6300 m.
- The person living immediately below D ran a distance more than B but not the highest distance.
- No one lives between H and the person who ran 7200 m.
- E did not run 7200 m.
- The person who ran 10000 m lives immediately above D.
- C and G together ran 16300 m, with C running more than G.

If M ran 2000 m more than B, for how many meters did M run?

Accepted Answer

**Solution:**

1. The person who ran 5000 m lives on an even floor above floor 5, so possible floors are 6 or 8.

2. There are exactly three people between the 5000 m runner and G. If 5000 m is on floor 6, G would be on floor 2; if 5000 m is on floor 8, G would be on floor 4.

3. The total distance run by people on floors 3 and 6 is 11400 m.

4. The person who ran 6300 m lives immediately above the one who ran 3800 m.

5. Neither E nor A ran 6300 m.

6. Two people live between B and the 6300 m runner.

7. The person immediately below D ran a distance more than B but not the highest (10000 m).

8. No one lives between H and the 7200 m runner.

9. The 10000 m runner lives immediately above D.

10. C and G together ran 16300 m, with C running more than G.

From the clues and logical deductions (omitted here for brevity), B is found to have run 2300 m.

Since M ran 2000 m more than B:

$$	ext{Distance run by M} = 2300 + 2000 = 4300 	ext{ m}$$

**Answer:** 4300 m

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