# 2015 AMC 10B Problems/Problem 6

## Problem

Mahdi practices exactly one sport each day of the week. He runs three days a week but never on two consecutive days. On Monday he plays basketball and two days later golf. He swims and plays tennis, but he never plays tennis the day after running or swimming. Which day of the week does Mahdi swim?

$\textbf{(A) } \text{Sunday} \qquad\textbf{(B) } \text{Tuesday} \qquad\textbf{(C) } \text{Thursday} \qquad\textbf{(D) } \text{Friday} \qquad\textbf{(E) } \text{Saturday}$

## Solution

Marley does basketball on Monday and golf on Wednesday. Since there are four consecutive days between Wednesday and Monday exclusive, she must run on Tuesday. Thus, she must also run on Thursday and Saturday or Friday and Sunday. She can't run on Thursday and Saturday because she would have to do tennis after running, which is not allowed. Thus, she runs on Friday and Sunday, so she must do tennis on Thursday, so she swims on $\boxed{\mathbf{(E)}\ \mathrm{Saturday}}$

~savannahsolver