16. Peter always tells the truth or always lies on alternate days. One day, he made exactly four of the following five statements. Which one did he not make?
A I lied yesterday and I will lie tomorrow.
B I am telling the truth today and I will tell the truth tomorrow.
C 2024 is divisible by 11 .
D Yesterday was Wednesday.
E Tomorrow will be Saturday.
Solution
C

Statement (B) can only be made by a person who lies on that day. Looking at the statements (D) and (E), they cannot both be true. Therefore, we have at least two statements that are lies. Therefore Peter has not made four true statements. This means that Peter is lying today. However statement $(\mathrm{C})$ is true because $2024=11 \times 184$. So this is the statement that Peter did not make.