TMUA Beyond Horizon Set 3 Paper 2 · Question 20

Consider the triangular array of numbers with $0,1,2,3,\ldots$ along the sides and interior numbers obtained by adding the two adjacent numbers in the previous row. Rows $1$ through $6$ are shown:

\begin{array}{ccccccccccc} &&&&&0&&&&&\\ &&&&1&&1&&&&\\ &&&2&&2&&2&&&\\ &&3&&4&&4&&3&&\\ &4&&7&&8&&7&&4&\\ 5&&11&&15&&15&&11&&5 \end{array}

Let $f(n)$ denote the sum of the numbers in row $n$ . What is the remainder when $f(100)$ is divided by $100$ ?

12

30

50

62

74

examday

Beyond Horizon Set 3 Paper 2 · Q20