Question

There is a row of 15 trees in a garden. Starting from the first tree, a gardener marked every second tree, then, on his way back, he marked the first tree, and then every third tree. How many trees are left without a mark?

Answer 1

Answer:  5

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Explanation:

The gardener starts at the first tree and then marks every second tree. So they'll skip a tree each time.

The set of trees he marks has the labels {1,3,5,7,9,11,13,15}. Basically it's the set of odd whole numbers between 1 and 15. Or you could notice that we add on 2 each time we need another tree to mark.

Then he goes back to the first tree and marks every third tree. So we have this new set: {1,4,7,10,13}. Start at 1 and add 3 each time to generate a new item.

Union the two sets mentioned and you'll get {1,3,4,5,7,9,10,11,13,15}

We see that the following trees aren't marked: {2,6,8,12,14}

There are  5   items in that last set.

Side note: The trees with labels {1,7,13} have been marked twice. There's a gap of 6 units between each adjacent label.

Answer 2

Answer:2

Step-by-step explanation:

15/3 = 5

15/2 = 7.5

+1

= 13

15 - 13 = 2