Wednesday, March 09, 2011

Ice Cream Conundrum

It's been a long time since I've had to turn to the cyber world for help with math, but here we are today, hat in hand.

Here's the problem:

Every afternoon the three little pigs take an ice cream break. They head to the closest ice cream shop, where each orders a double-dip cone. There are only two kinds of double dips that the pigs ever order. It's either a double-dip vanilla cone or a licorice-chocolate combination.

If pig #1 orders vanilla-vanilla, then pig #2 orders the other. Either pig #1 or pig #3 orders vanilla-vanilla, but they never do so on the same day. Pig #2 and Pig#3 never both order the licorice-chocolate combination the same day.

Which of the three little pigs ate a vanilla-vanilla cone yesterday and will order a licorice-chocolate cone today?
Sweetling and I think that there is a misprint in the book. We can come up with only one scenario of orders which meet all the criteria of the problem.

Help?

3 comments:

Nora MacFarlane said...

The way it's worded is confusing. How can both pig #2 and pig #3 order the opposite of pig #1, yet not order the same thing?

Guy said...

Rule #1: Each pig either orders double-dip vanilla or licorice-chocolate.

Rule #2: If pig #1 orders vanilla-vanilla, then pig #2 orders the other.

Rule #3: Either pig #1 or pig #3 orders vanilla-vanilla, but they never do so on the same day.

Rule #4: Pig #2 and Pig #3 never both order the licorice-chocolate combination the same day.

Question: Which of the three little pigs ate a vanilla-vanilla cone yesterday and will order a licorice-chocolate cone today?


Solution:

Suppose Pig #1 orders double-dip vanilla. Then pig #2 must order licorice-chocolate, because of rule #2. Pig #3 must also order licorice-chocolate because of rule #3. However, Pig #3 must not order licorice-chocolate because of rule #4.

Therefore, Pig #1 can never order double-dip vanilla.

Therefore, Pig #1 always orders licorice-chocolate. Rule #2 doesn't come into play, and by rule #3, pig #3 always orders double-dip vanilla. Rule #4 doesn't apply either. Therefore, Pig #2 can switch back and forth at will, and is the only possible pig that can answer the question.

Mrs Random said...

OH!!!!

I just called Sweetling in to read Guy's solution. We were both misinterpreting rule two....thinking that pig two always ordered the opposite of pig one rather than pig two only orders the opposite of pig one if pig one orders vanilla.

Thank you!!!!!