Question

There are 24 tokens numbered 1 to 24 that are put into a box. A person is blindfolded and asked to take out as many tokens as he wishes till he is definite that he has at least one pair that adds up to 24. What is the largest number of tokens that he needs to remove?

Answer 1

@campbell_st @mathslover @mathstudent55

Answer 2

13

Answer 3

pls explain

Answer 4

I'll let someone else explain it...

Answer 5

suppot me guys!

Answer 6

Worst Case Scenario: You pull out the numbers 1,2, 3, 4, ..., 9, 10, 11, 12

Note: you pick those numbers in any order

None of those numbers can pair up to add up to 24 or over. So that's why you need to pick a 13th number to be guaranteed to have a pair add up to some number 24 and over.

Answer 7

thanks!

Answer 8

If it's exactly 24, then make a 24 x 24 table and count how many sums of 24 you get (eg: 11+13=24, 12+12 = 24, etc)

that will help you find the min amount of numbers needed to pull out

Answer 9

@jim_thompson5910 12+12 isn't a possibility, they're numbered 1-24. This problem seems much more complex if the numbers need to add to exactly 24, and "till he is definite that he has at least one pair that adds up to 24" so the guy has to be sure.

Answer 10

oh right, he pulls out a number and it isn't put back

Answer 11

But i guess we aren't looking for # of ways it can happen, just number of tokens pulled, which makes it simpler.

Answer 12

1 2 3 4 5 6 7 8 9 10 11 12
24 23 22 21 20 19 18 17 16 15 14 13

Answer 13

Each column above represents a sum of 24.
If he takes tokens numbered 1 through 12 and 24, he still does not have a single pair that adds up to 24, so he needs to take at least 14 tokens to be sure one pair adds up to 24.

Answer 14

Earlier, when I answered 13 tokens, I thought the problem was asking for a pair of tokens that added to at least 24, but it states one pair that adds up to 24. If this means that the pairs adds up to exactly 24, then the answer is 14 tokens.

Answer 15

Nice. Looks good.

Answer 16

@agent0smith Thanks