14. Each box in the strip shown is to contain one number. The first box and the eighth box each contain 2021. Numbers in adjacent boxes have sum $T$ or $T+1$ as shown. What is the value of $T$ ?

A 4041
B 4042
C 4043
D 4044
E 4045
Solution
E

Starting on the left, the first two boxes add to $T$ so the second box is $T-2021$. The second and third boxes add to $T+1$ so the third box is 2022 . Continuing in this way, the numbers obtained are $T-2022,2023, T-2023$, and 2024. The final box is 2021 and the final two boxes have total $T$. So $T=2024+2021=4045$.