SIN Bin

2018, problem 12

Bill the sausage maker is collecting his sausage, which has been curing all year on a series of clotheslines in the barn. When he hung the sausage, he did so such that each of the four flavours is positioned 0.5m apart vertically; chorizo at top, then summer, then garlic, and finally kielbasa 4.0m above the floor. Bill has a 10m long ladder, which slides on the smooth floor, such that when he climbs the ladder, the lowered slides away from the wall with the same speed that he climbs.

If Bill (height 2m) starts the ladder off vertically against the wall and begins climbing, what is the maximum number of sausage types that he can grab while moving up the ladder with constant speed?

Illustration showing the height of clotheslines in the barn, with a ladder leaning against the wall

(a) 0

(b) 1

(c) 2

(d) 3

(e) 4