A farmer decides to plant a row of trees along one side of a road. He decides to plant one tree every 15 metres. If the road is 460 metres long, what is the maximum number of trees the farmer could plant?

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Comments

StenJul 28

Thanks, I always mess up these fencepost-type questions. The 460/15 part is easy but then I second-guess whether to add one.

BhavyaAug 7

Same here. I think the trick is whether a tree goes at the very start of the road or not.

KartikAug 27

Wait, does the row have to start exactly at one end of the road? If yes I can see why there's an off-by-one, but the wording is a little ambiguous.

GuidoSep 8

I think 'along one side of a road' implies the row runs the whole length. The question asks for the maximum, so assume you can use both endpoints.

AndrewSep 18

Classic trap. 460/15 = 30 with a remainder, so some people pick 30. But maximum means you can squeeze one more at the start. Nice question.

AmmuOct 1

Exactly — the remainder is what makes it possible to still fit that extra tree.

SamuelAug 5

Got 31 pretty quickly. Interval problems are usually just total distance divided by spacing, then +1 if both ends are included.

What this question tests

Your ability to spot and extend arithmetic and geometric sequences and work with recursive definitions.

Off-by-one errors in indexing (a₀ vs a₁) or confusing an arithmetic difference with a geometric ratio.