S2:S100
Halimat is a pro with cards, today, she is given a deck of 52 cards from her friend Chinelo, and she knows in that pile are 13 cards that are facing up and the rest are facing down in a random order. Halimat is blindfolded and cannot see the cards. She needs to create two piles with the same number of cards facing up.
Question:
How can she do it? Explain
Halimat needs to take the first 13 cards from the top and simply flip them over.
ReplyDeleteIf you took the first 13 cards from the top and let’s say, there are nine facing-up cards in that first pile. This means that the remaining pile would have only 4 facing-up cards as we know from the beginning, that 13 out of the 52 cards were facing up. If you flip the first pile over, four cards will be facing up and nine will be facing down.
Her job is to separate this deck of cards into two piles of cards that both have the same number of face-up cards. Both piles must contain at least one card.
ReplyDeleteThe first she is to do is to simply cut the deck in half by counting 26 cards. Then she cannl split 13 cards evenly. The best she could hope for would be 6 face-up cards in one pile and 7 in another. This means that there must be some cards she have to flip over.
Next, she should thinkabout flipping cards over one at a time and wondered when she should stop.what if she stopped at 13?
It turns out that this is a solution to the problem! Indeed, she could count out any 13 cards in the deck, flip them over to form a pile, and she would solve the problem.
Halimat will have to take the first 13 cards from the top, assuming there are nine facing-up cards in that first pile. This means that the remaining pile would have only 4 facing-up cards as we know from the beginning, that 13 out of the 52 cards were facing up. If she flips the first pile over, four cards will be facing up and nine will be facing down.
ReplyDeleteIn essence, Halimat needs to take the first 13 cards from the top and simply flip them over.
Halimat can accomplish this by using a simple and strategic method. She can divide the deck into two piles of 26 cards each. Then she can flip all the cards in one of the piles.
ReplyDeleteAt this point, she knows that both piles have 26 cards facing down. She can now pick up one of the piles and put the two piles together. When she turns the deck over, she will have 13 cards facing up in each pile.