at a farewell party, people were asked to guess how many marbles there were in a box. no one guessed correctly, but the nearest guesses were 171, 177, 186 and 190. the correct number of marbles was one unit away from one of the closest guesses, three units away from another, ten units away from the third and sixteen units away from the remaining closest guess. how many marbles were there in the box?

Let's analyze the information from the farewell party marble guessing game:

• No one guessed the exact number of marbles.
• The nearest guesses were 171, 177, and 18.

What can we infer?

1. Nearest guesses are close to the actual number
   Usually, "nearest guesses" means these guesses were the closest to the true number of marbles.

2. 171 and 177 are close to each other, 18 is far apart
   The guesses 171 and 177 are only 6 apart, while 18 is much lower. This suggests the actual number might be near 171 or 177 rather than near 18.

3. No one guessed correctly
   The actual number is not 171, 177, or 18.

Possible actual number of marbles

Since 171 and 177 are the closest guesses, the actual number is likely between these two numbers but not equal to either. The guess 18 is likely a distant guess and less relevant.

• The actual number could be 172, 173, 174, 175, or 176.

Conclusion

The most reasonable estimate for the number of marbles is between 172 and 176 , assuming the "nearest guesses" are the closest guesses without an exact match. If you want, I can help you analyze this further or suggest ways to determine the exact number!