Farmer's Market

[coolgames]

A farmer has to move 100 pumpkins from his farm to a market. He uses carts for carrying the pumpkins. Each cart can hold a maximum of 10 pumpkins. There are 10 toll stations on the way to the market. They charge 1 pumpkin per each cart as fee. How many pumpkins can he sell in the market ??

Have Fun,
Coolgames

Note: All this is genetated by ME...

[RedSon]

A farmer has to move 100 pumpkins from his farm to a market. He uses carts for carrying the pumpkins. Each cart can hold a maximum of 10 pumpkins. There are 10 toll stations on the way to the market. They charge 1 pumpkin per each cart as fee. How many pumpkins can he sell in the market ??

Have Fun,
Coolgames

Note: All this is genetated by ME...

This is the same as:
A farmer has 10 pumpkins that he wants to sell, each of his carts can hold 1 pumpkin. There is 1 toll station on the way to the market, it charges 1 pumpkin per each cart as a fee. Simple to figure out now, no?

[coolgames]

not exactly..
just if you reduce the numbers, you will deffinately end up with a WRONG answer...

[kadghar]

not exactly..
just if you reduce the numbers, you will deffinately end up with a WRONG answer...

i think they are 32

since he can leave carts in the toll stations

[jkmyoung]

Well, if he only uses the carts:
Start
100 pumpkins, 10 carts

Does he have to pay the toll as soon as he reaches the toll booth or after? Here we assume as soon as.

1st toll 10 pumpkins. Remaining:
90 pumpkins. 9 carts, ditch one. (he'll be able to get it on his way back)

2nd toll 9 pumpkins. Remaining:
81 pumpkins. 9 carts. Here, he might as well ditch 1 pumpkin and 1 cart for later too, leaving 80 pumpkins. 8 carts

3rd toll 8 pumpkins. Remaining:
72 pumpkins, 8 carts.

4th toll 8 pumpkins. Remaining
64 pumpkins, 7 carts, ditch 1 cart.

5th toll 7 pumpkins. Remaining:
57 pumpkins, 6 carts, ditch 1 cart.

6th toll 6 pumpkins. Remaining
51 pumpkins, 6 carts. Ditch an extra pumpkin and cart leaving
50 pumpkins, 5 carts.

7th toll 5 pumpkins. Remaining:
45 pumpkins, 5 carts.

8th toll 5 pumpkins. Remaining:
40 pumpkins 4 carts. ditch 1 cart.

9th toll 4 pumpkins. Remaining:
36 pumpkins 4 carts.

10th toll 4 pumpkins. Remaining:
32 pumpkins. 4 carts.

The farmer can make it with 32 pumpkins total.
Left at each of the toll booths:
1: 10 pumpkins toll, 1 cart
2: 9 pumpkins toll, 1 cart, 1 extra pumpkin
3. 8 pumpkins
4. 8 pumpkins, 1 cart
5. 7 pumpkins, 1 cart
6. 6 pumpkins, 1 cart, 1 extra pumpkin.
7. 5 pumpkins.
8. 5 pumpkins, 1 cart.
9. 4 pumpkins.
10. 4 pumpkins.

What does he do with the extra pumpkin left at the 2nd and 6th station? smash them.
Why not just carry the extra pumpkin to the next station and pay with it for the extra cart? I don't know, but I'm against giving extra taxes to the man, lol.

If the farmer only has to pay to cross with the cart:
1: pay 9 pumpkins, leave an extra pumpkin and cart behind. Continue with
90 pumpkins, 9 carts
2: pay 9 pumpkins. Continue with
81 pumpkins, 9 carts
3: pay 8 pumpkins. Leave a cart behind. Continue with:
73 pumpkins, 8 carts
4: pay 7 pumpkins. Leave a cart behind. Continue with:
66 pumpkins, 7 carts.
5: pay 6 pumpkins, Leave a cart behind. Continue with:
60 pumpkins, 6 carts.
6: pay 6 pumpkins. Continue with:
54 pumpkins, 6 carts.
7: pay 5 pumpkins. Leave a cart behind. Continue with:
49 pumpkins, 5 carts.
8: pay 5 pumpkins. Continue with:
44 pumpkins, 5 carts.
9: pay 4 pumpkins. Leave a cart behind. Continue with:
40 pumpkins, 4 carts.
10: pay 4 pumpkins. Left with:
36 pumpkins.
A 4 pumpkin difference if the farmer is allowed to do it this way.

I wonder what would happen if the toll booths would be willing to take carts instead of a pumpkins

[RedSon]

I wonder what would happen if the toll booths would be willing to take carts instead of a pumpkins

Good question, what is the answer then if the toll booths will take either a pumpkin or cart as payment, also, you forgot to consider how the farmer will get back to his home with these carts, or do you assume that he only has himself and one cart to take him back, while leaving the rest at the market?

[kadghar]

Good question, what is the answer then if the toll booths will take either a pumpkin or cart as payment, also, you forgot to consider how the farmer will get back to his home with these carts, or do you assume that he only has himself and one cart to take him back, while leaving the rest at the market?

that's true!!

he'll have to sell only 22 pumkins and keep 10 and a cart to go back home.

or may be the toll stations fee is 1 pumpkin for the round trip.

[coolgames]

good work... i've never had anyone explain it very eloberately before..


Coolgames

[YarrOfDoom]

I would have tought of this as:

He needs to get 100 pumpkins to the market, so he takes some extra to pay the fee and so he arrives witth 100 pumpkins.

[coolgames]

I would have tought of this as:

He needs to get 100 pumpkins to the market, so he takes some extra to pay the fee and so he arrives witth 100 pumpkins.

why would think that ??
the Q' clearly explains...

if it is not clear to you, i am sorry.
Coolgames

[Banfa]

What does he do with the extra pumpkin left at the 2nd and 6th station? smash them.
Why not just carry the extra pumpkin to the next station and pay with it for the extra cart? I don't know, but I'm against giving extra taxes to the man, lol.

I would have thought the obvious answer is to leave the at home, only setting out with 98 pumpkins then when he gets home he can have pumpkin pie for tea.

[coolgames]

I would have thought the obvious answer is to leave the at home, only setting out with 98 pumpkins then when he gets home he can have pumpkin pie for tea.

** laughs ** Yummy..
my mom never makes me yummy stuff...