Ice cream cones come in three cone types: plain, sugar, and waffle, and in fourteen flavours: vanilla, chocolate, rocky road, mint chocolate chip, strawberry, pralines and cream, bubble gum, butter pecan, mud pie, peanut butter crunch, almond fudge, coffee, chocolate chip, and banana royale.
You want to buy a two-scoop cone. How many are there to choose from?
Warning: only 16% of the submitted answers were correct (297 out of 1841) when it was presented as Problem of the Week at Columbus State University.
February 18th, 2010 at 7:09 am
Hmm… with just a 16% success rate I’m probably about to make a fool out of myself but here’s a shot at it:
You have 3 cones to choose from. For each cone, scoop 1 can be one of 14 flavors. 3×14 = 42 possibilities. For each one scoop cone, scoop 2 can be one of 14 flavors. 3x14x14 = 588 possibilities.
February 18th, 2010 at 4:27 pm
There are 14*13/2 ways to choose the flavours for a two-scoop cone with different flavours. This is 7*13=91.
There are 14 ways to choose the flavour for a cone with only one flavour. Total, 91+14=105.
Independently of this, you can choose a cone type from among 3 types. So there are 3*105=315 possibilities.
February 19th, 2010 at 9:05 am
Michael’s and Richard’s different answers just illustrate the fact that the problem is poorly specified. Is a chocolate and vanilla cone different than a vanilla and chocolate? Can you get both scoops the same flavor?
February 19th, 2010 at 9:42 am
“…the problem is poorly specified…”
In my opinion all problems are poorly specified. They can be interpreted in n ways and then 1. That doesn’t mean that they are bad. That something is wrong with them. One has to interpret them, and state ones interpretation, and then solve it. If one has many interpretations, then one has many problems to solve.