Highgate Maths question

[Barnetmamma]

Can someone help with this maths question?

James has 15 sweets in his pocket. He has 7 red sweets, 6 blue sweets, and 2 pink sweets. Without looking, he removes some sweets from his pocket and places them on the table. What is the smallest number of sweets he should remove to guarantee that he has at least one sweet of each colour?

DD and I interpreted it differently. She thought it was related to having one of each colour in the ones he removed (she came up with 14), whereas I thought, it was about having one of each colour left in his pockets (I came up with 1).

Not sure which one of us is right... or perhaps even both wrong?

[Guest55]

I'd agree with you - if you take more than 1 then you might take all the pink sweets.

[loobylou]

I read it as needing to guarantee one sweet of each colour on the table - so 14.
I can see that your (and G55) interpretation could be right as well but I would not have thought of that.
If that's the wording of the question then I don't think it's very clear.

[Stokers]

I think if it was sweets remaining in pocket, the word would be 'could' not 'should'. But, I agree - there should be an indication of whether it is sweets remaining in pocket or put on table

[nyr]

I reckon it's 14 sweets, as the answer to "What is the smallest number of sweets he should remove to guarantee that he has at least one sweet of each colour?" would be:
14 if it referred to sweets on the table,
(probably) 0 if it referred to sweets in his pocket but this is unlikely to be the answer the examiner was expecting.

My feeling is that many indie maths papers have to be treated with some caution as I'm not sure that the questions are always carefully thought.

[Guest55]

If it doesn't mean the number taken from the sweets in his pocket then it is an appalling question.

[Surferfish]

I think the answer they are looking for is 14, and that they probably are trying to say "What is the smallest number of sweets he should remove to guarantee that he has at least one sweet of each colour ON THE TABLE" rather than "What is the smallest number of sweets he should remove to guarantee that he has at least one sweet of each colour LEFT IN HIS POCKET". But agree that it is a very badly worded question.

As mentioned if they were talking about the sweets left in his pocket the answer would actually be zero, which is why I don't think this is the interpretation they meant. It also says he removes SOME sweets which implies more than one.

[Guest55]

He can remove one and be sure to have some of each type in his pocket.

James should not be eating sweets!