Question 12
There is a road from town A to town B with a line of villages. Adjacent villages are 10 km apart; the first village is 20 km from A and the last is 20 km from B. Each village has some statues. Arthur travels from A to B and must travel at least 20 km per day. If he stops at a village, he stays there that day and resumes his journey toward B the next day, so he misses some villages. He wants to visit as many statues as possible. For example:
- A 4 3 4 3 B: he stops at villages 1 and 3.
- A 2 4 5 4 B: he stops at villages 2 and 4.
- A 5 4 2 3 B: he stops at villages 1 and 4.
In each case he visits 8 statues. For the following line, what is the maximum number of statues he can visit?
A 3 1 4 1 5 9 2 6 5 3 5 8 9 8 7 5 2 B
- A 4 3 4 3 B: he stops at villages 1 and 3.
- A 2 4 5 4 B: he stops at villages 2 and 4.
- A 5 4 2 3 B: he stops at villages 1 and 4.
In each case he visits 8 statues. For the following line, what is the maximum number of statues he can visit?
A 3 1 4 1 5 9 2 6 5 3 5 8 9 8 7 5 2 B