Seven persons E, F, G, H, S, T, and U buy seven different items — Tie, Coat, Ring, Nail paint, Shirt, Diary, and Goggles — on different days. Each person buys exactly one item on one day.

Given the following conditions:

- Four persons buy items between E and the one who buys the Tie.
- The person who buys the Coat buys immediately after the one who buys the Tie.
- Two persons buy items between H and the one who buys the Tie.
- T buys immediately after H.
- F buys his item immediately after the one who buys the Diary.
- Two persons buy items between the one who buys the Coat and the one who buys the Shirt.
- S buys the Ring.
- Goggles were bought immediately after E.
- Two persons buy items between the one who buys the Ring and the one who buys the Diary.
- U buys his item before G.

**Question:** How many persons buy items between S and F?

Question

Seven persons E, F, G, H, S, T, and U buy seven different items — Tie, Coat, Ring, Nail paint, Shirt, Diary, and Goggles — on different days. Each person buys exactly one item on one day.

Given the following conditions:

- Four persons buy items between E and the one who buys the Tie.
- The person who buys the Coat buys immediately after the one who buys the Tie.
- Two persons buy items between H and the one who buys the Tie.
- T buys immediately after H.
- F buys his item immediately after the one who buys the Diary.
- Two persons buy items between the one who buys the Coat and the one who buys the Shirt.
- S buys the Ring.
- Goggles were bought immediately after E.
- Two persons buy items between the one who buys the Ring and the one who buys the Diary.
- U buys his item before G.

**Question:** How many persons buy items between S and F?

Accepted Answer

**Solution:**

Let's analyze the given information step-by-step to find the order of persons and items:

1. There are 7 persons and 7 items, each person buys one item on a different day.

2. Four persons are between E and the one who buys the Tie. So the positions of E and Tie differ by 5.

3. The Coat is bought immediately after the Tie.

4. Two persons are between H and the Tie.

5. T buys immediately after H.

6. F buys immediately after the person who buys the Diary.

7. Two persons are between the Coat and the Shirt.

8. S buys the Ring.

9. Goggles are bought immediately after E.

10. Two persons are between the Ring and the Diary.

11. U buys before G.

**Step 1: Assign positions to Tie and E**
- Since 4 persons are between E and Tie, their positions differ by 5.
- Possible positions for Tie and E are (1,6) or (2,7) or vice versa.

**Step 2: Place Coat immediately after Tie**
- Coat is next to Tie.

**Step 3: Two persons between H and Tie, and T immediately after H**
- So H and Tie are 3 positions apart.

**Step 4: Goggles immediately after E**

**Step 5: S buys Ring**

**Step 6: Two persons between Ring and Diary**

**Step 7: F immediately after Diary**

**Step 8: Two persons between Coat and Shirt**

**Step 9: U before G**

By testing possible arrangements, the sequence that satisfies all conditions is:

| Position | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|----------|---|---|---|---|---|---|---|
| Person   | U | S | H | T | Tie Buyer | Coat Buyer | E |
| Item     | ? | Ring | ? | ? | Tie | Coat | ? |

F and Diary must be placed such that F is immediately after Diary, and two persons are between Ring and Diary.

After placing all, the order of persons is:

1. U
2. S (Ring)
3. H
4. T
5. G (Tie)
6. F (Coat)
7. E (Goggles)

Diary is bought by person at position 3 or 4 to satisfy conditions with F.

Counting persons between S (position 2) and F (position 6): positions 3, 4, 5 — three persons.

**Answer:** Three persons buy items between S and F.

Answer

Answer

Answer