## Problem of the Day #60: HUM Field Trip RefreshmentsMay 18, 2011

Posted by Seungln in : potd , trackback

Albert, Alex, Arjun, Saketh and SeungIn are travelling together on a HUM field trip. They each have a certain amount of money and wish to purchase food.

The following list shows how much money each of them has, in dollars.
Albert – $5.00 Alex –$10.00

Arjun – $5.00 Saketh –$10.00

SeungIn – $10.00 They come across a rather expensive refreshment store with very limited choices of food. The following list shows how much each item costs. Bagel –$1.95

Orange juice – $2.25 Bottled water –$2.95

Chicken wings – $3.75 Soda (12 oz.) –$4.15

Hot dog – $4.75 Hamburger –$5.95

Slice of cheese pizza – $6.25 Soda (20 oz.) –$6.95

Slice of pepperoni pizza – \$7.25

The crew decide to gather up the money and buy food for the whole group. However, there are several conditions that must be met.

1. Albert is not thirsty at all, and will not get a drink.

2. Alex, a runner, is thirsty and wants either bottled water or 12 oz. soda.

3. Alex likes pizzas, and, if affordable, will get one. (He likes both types, and does not care which one the group gets for him.) He is, however, also fine with not getting one.

4. Arjun is vegetarian and cannot eat anything with meat. (i.e. he cannot order chicken wings, a hot dog, or a slice of pepperoni pizza.)

5. Arjun likes bagels, and, if affordable, will demand that the group buys one. He will probably be disappointed if he doesn’t get one.

6. Saketh, who always brushes his teeth, refuses to drink orange juice because orange juice and fluorine make a terrible taste.

7. Saketh likes hot dogs, and, if affordable, will ask the group to buy one. He brought extra food just in case, however, and does not require it.

8. SeungIn’s throat is easily dehydrated, so he must have the 20 oz. soda.

9. Unless stated above, each person will, if affordable, get a drink and a food for himself.

10. Nobody in the group wants to owe someone more than a dollar.

In how many ways can the group order food in such a way that all ten of these conditions will be satisfied, and Arjun won’t be disappointed?