In detail

Candy bag

Candy bag

We have a bag that contains a total of 71 delicious candies of different flavors. There are twice as many lemon candies as strawberry candies, orange candies are one less than strawberry candies and mint candies are six candies less than lemon candies.

How many delicious candies will you have to extract at least from the bag (without looking) to be sure you can eat two different flavors?

Solution

There are twice as many lemon as strawberry candies, then adding the lemon and strawberry ones, we have a multiple number of 3.

Those of orange are one less than those of strawberry, therefore, if we added one more (72 in total), there would be the same ones of strawberry that of orange. And in total we would have a multiple of 4.

Those of mint are six less than those of lemon, that is to say if we added 6 (78 in total), we would have the same ones of lemon that of mint, strawberry and orange. That means that if we divide the 78 candies by 2, we would have 39, which are those of lemon and strawberry, and dividing by 3, we would get 13, which are those of strawberry.

That is, there are 13 strawberry, 26 lemon, 12 orange and 20 mint. In total 13 + 26 + 12 + 20 = 71.

If we want two to be different, the worst situation we can have is that we take out the 26 lemon in a row, but if we take 27 candies, necessarily two of them will have different flavor.