A number of bulbs are placed in a row. 4 of them are working. Each pair of the 4 working bulbs has a different number of bulbs (working or non-working) between them. What is the minimum possible value for the number of bulbs?

To have a different number of bulbs between each pair of working bulbs, we need to place the working bulbs in such a way that no two pairs have the same number of bulbs between them. The smallest sequence that satisfies this condition is to have 0, 1, 2, and 3 non-working bulbs between the working ones.

Here’s the minimum arrangement:

W - N - W - NN - W - NNN - W

So, we have:

0 bulbs between the first and second working bulbs

1 bulb between the second and third working bulbs

2 bulbs between the third and fourth working bulbs

3 bulbs between the fourth and fifth working bulbs

Counting all the bulbs, we have 4 working bulbs (W) and 6 non-working bulbs (N), which gives us a total of 10 bulbs.

Therefore, the minimum possible number of bulbs is 10.

greentoowon greentoowon · Answer 2 · 2024-04-28T12:11:10-04:00

1. Start with the fact that there are 4 working bulbs.

2. Arrange these working bulbs with different numbers of non-working bulbs between them.

3. To minimize the total number of bulbs, place 1 non-working bulb between the first pair of working bulbs.

4. Place 2 non-working bulbs between the second pair of working bulbs.

5. Place 3 non-working bulbs between the third pair of working bulbs.

6. Place 4 non-working bulbs between the fourth pair of working bulbs.

7. Add up the working bulbs and non-working bulbs: 4 working + 1 + 2 + 3 + 4 = 14 bulbs in total, which is the minimum possible value.