Camp Counselor and Campers Seating Arrangement Puzzle

In a summer camp, a camp counselor and six campers are to be seated along a picnic bench. The counselor must be seated in the middle, and a specific camper who has a tendency to engage in food fights must sit to the counselor's immediate left. The question is, in how many ways can this seating arrangement be done?

Solution:

To solve this puzzle, we first need to determine the total number of ways to arrange the camp counselor and the six campers along the picnic bench.

Since the camp counselor must sit in the middle, there are 6 campers left to be arranged around the counselor. The camper who has a tendency to engage in food fights must sit to the counselor's immediate left, which means this specific camper occupies a fixed spot.

Therefore, we have 1 way to seat the food-fighting camper next to the counselor. The remaining 5 campers can be arranged in 5! (5 factorial) ways. Since the food-fighting camper can also be seated to the counselor's right, we need to multiply the total by 2 to account for this arrangement.

So, the total number of ways to seat the camp counselor and six campers along the picnic bench is 1 (for the food-fighting camper) * 5! (for the remaining campers) * 2 (for the two possible seating arrangements of the food-fighting camper) = 1 * 120 * 2 = 240.

Conclusion:

Therefore, the seating arrangement of the camp counselor and six campers can be done in 240 different ways, considering the specific requirement of seating the food-fighting camper to the counselor's immediate left.