I've been going in circles with this question which belongs to certainty about something. The original source of this problem is unknown. I found it in a textbook who doesn't have an author but rather a collection of riddles about combinatorics and different problems.
The problem is as follows:
A porcelain jar is filled with a set of sphere candies. The baker made them in a peculiar condition, so that one half of the ball shaped candy has a color different from its other half. 24 of those candies has one side colored blue (due a blueberry flavor) and the other half is colored green (due a pear flavor), 30 has one half green and the other half red (due strawberry flavor), 28 has one half red and the other white (due mint flavor), 40 has one half white and other half orange (due orange flavor) and 35 candies has one half orange and the other half blue. How many of these candies must be taken out from the jar at random and at least to affirm that 7 candies share the same color? (Assume that you are not allowed to have a peek inside the jar).
The choices given are:
I don't understand "to affirm that 7 candies share the same color". Does it mean I should count other colors whose one half also coincides with the first group?
I'm aware that when there is some uncertainty about something, the procedure is to assume the most difficult to happen scenario or event, and from then on ruling out possibilities until we can assure that our next pick will guarantee what we need.
Examples I saw show this for objects which share entirely one color or shape. But what if they have split colors?
Should I understand that they ask to match the identical ones or match the objects (the candies in this case) which have the same set of colors i.e red and white, with ones which one side red and other which have the other have white, but may have its opposing side with a different color? Can somebody clarify this for me?
In my attempt to solve this problem what I tried to do was this:
Since they ask for 7 candies, then the hardest possibly to happen scenario might be:
6 white and orange +
6 green and red +
1 of any of the remaining group
(could be blue and green or red and white or orange and blue)
Should I count the other half as color to meet the asked condition for 7 candies sharing the same color?
Supposedly the answer is 16 but I don't know how to get there. How to justify this?