Questions: I live in a small street with 6 houses. One day 35 letters were delivered in my street and I received more letters than anyone else. What is the smallest number of letters I could have received? (A) 5 (B) 6 (C) 7 (D) 8

Solution Steps

To find the smallest number of letters I could have received, we need to distribute the 35 letters among the 6 houses such that I receive more letters than anyone else. We can start by distributing the letters as evenly as possible and then adjust to ensure I receive the most.

1. Distribute the letters as evenly as possible among the 6 houses.
2. Ensure that I receive more letters than any other house.

We have a total of \( 35 \) letters to distribute among \( 6 \) houses. First, we calculate the base number of letters each house would receive if distributed evenly: \[ \text{base\_letters} = \left\lfloor \frac{35}{6} \right\rfloor = 5 \] This means each house would initially receive \( 5 \) letters.

Next, we find the number of remaining letters after the initial distribution: \[ \text{remaining\_letters} = 35 \mod 6 = 5 \] This indicates that there are \( 5 \) letters left to distribute.

To ensure that I receive more letters than any other house, I need to receive at least one more letter than the maximum any other house can receive. The maximum any other house can receive is: \[ \text{max\_other\_house} = \text{base\_letters} + 1 = 6 \] Thus, I need to receive: \[ \text{min\_letters\_received} = \text{base\_letters} + 1 + 1 = 7 \]

Final Answer