Please help me!?

Question

A man had a basket containing 25 potatoes. As a recreation for his son, he placed the potatoes on the ground in a straight line so that the distance between the first and the second was 1 yard, between the second and the third was 3 yards, between the third and the fourth was 5 yards and so on – an increase of 2 yards for each successive potato laid down. The basket was placed on the ground next to the first potato. The boy was asked to pick up the potatoes one at a time and place them in the basket, without moving the basket. How far will the boy have to travel to pick them all up?

Hint: answer the question for 2 potatoes, then for 3, then 4 and so on until a pattern in the answers is found.


Okay so its really late and i really need help on this problem. If you could explain to me how you got your answers i would really appreciate it =)

Answer 1

The hint is helpful. Set a chart like this

number distance
of..............to get them
potatoes

1.....................0
2......................1
3.....................4
4.....................9
5....................16
6....................25

You can now see the pattern.

Answer 2

To get
potato 1 = 0
potato 2 = (1) * 2 = 2
potato 3 = (1+3) * 2 = 8
potato 4 = (1+3+5) * 2 = 18
potato 5 = (1+3+5+7) * 2 = 32
note the pattern
(1) = 1^2
(1+3) = 4 = 2^2
(1+3+5) = 9 = 3^2
(1+3+5+7) = 16 = 4^2
The answer will be
2 * (0^2 + 1^2 + 2^2 + 3^2 + 4^2 + 5^2 + ... + 24^2)

Answer 3

1 potato 2 potato 3 potatato 4

Answer 4

1 potato-2 yards
2 potatoes-6 yards
3 poatoes-10 yards
4 potatoes-14 yards
you add 4 each time...
5-18
6-22
7-26
8-30
9-34
10-38
11-42
12-46
13-50
14-54
15-58
16-62
17-66
18-70
19-74
20-78
21-82
22-86
23-90
24-94
25-98
add all of them together
1250 yards