Candy- Quantity and Quality

There are 8 red candy, 5 blue candy, 4 yellow candy, and 3 green candy. Tom picked out 3 pieces of candy, and two of them were the same. The one that he picked less of was green, and none of them were red. He also did not get introduced to the yellow candy, because the teacher forgot about them. Bob picked it after him and all of them were the same, but the quantity is over 5. Jeff picked 5 pieces of candy, three of them blue, two of them green. The last person to pick was Tim and he picked 5 pieces of candy, 2 red and 3 yellow. What color and quantity are left?

Bonus: Jeff's quantity and color are unknown as well. What color and quantity are left after?

2 blue 3 red 1 yellow 1 green

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1 solution

I am going to explain the answer here. "There are 8 red candy, 5 blue candy, 4 yellow candy, and 3 green candy." These are the quantity and quality of the candy. The pieces of candy that Tom picked out were two blue and one green because that makes sense since he did not get introduced to the yellow and red, and green is his favorite color. He does not want to eat it too much. That makes the quantity change to 3 blue and 2 green. Then Bob chose more than 5 candy but all one color. We can assume this red because that is the only one where there is more than 5. That decreases the red count to 2 red candy. Jeff picked three blue and two green. That decreases blue and green to nothing. So the ones that are left are 2 red and 4 yellow which makes it that Tim decreases it all the way to zero for red and one left for yellow.

Answer: 1 yellow. Duh!

Hope you like this problem! This problem was the first one I made. Comment down below if I made a mistake or any other comments or suggestions on future problems.

Hmm....you just changed the question. Let's see if it makes sense now. It didn't initially. (Among other things you had two guys named Jeff.)

Richard Desper - 1 year ago

Yeah. I realized. Also, I accidentally hit submit before putting everything down. I had typed the problem on a google document, and I copied and pasted some stuff, but then decided to change some stuff. In that hurry, I forgot to put a lot of key info. I am sorry. I am sort of new to using Brilliant.org for creating problems. I just do other people's puzzles most of the time as a school assignment.

It's still got a problem because the question says Jeff took six and your solution has Jeff taking five.

BTW, I would call this kind of problem "Combinatorics", not "Number Theory".

Richard Desper - 1 year ago

Well, @Eswar Gogineni , we are alike - my problems get abused because they are not right and your problems get abused because of typing issues. I, for one, find your problem flawless.

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