Pathway Math Problem (MPfG 2019 #10)
Math Prize for Girls 2019 #10 Problem: A 1*5 rectangle is split into five unit squares (cells) numbered 1 through 5 from left to right. A frog starts at cell 1. Every second it jumps from its current cell to one of the adjacent cells. The frog makes exactly 15 jumps. How many paths can the frog take to finish at cell 5? Solution: When we see such a problem, we automatically think of using some counting of permutations to help solve this, but actually, all we need is addition. 1 2 3 4 5 Step 1 1 Step 2 1 1 Step 3 2 1 Step 4 2 3 1 Step 5 5 4 Step 6 5 9 ...