Cards with cross
You have a stack of 23 cards. Each card has an image of a cross on one side
& an image of a circle on the other side. You know that 14 cards in the stack are
lying with the cross up, and therefore 9 cards are with the circle up. However,
you do not know in which order the cards are. Moreover, you are in completely dark
room,so you cannot see anything.
The Question: How can you, without seeing anything, divide the stack of
cards in two smaller stacks, in such a way that both stacks have the same
number of cards with a cross up?
A Hint : You can turn cards round
The Answer:
Take 14 cards from the stack. Of these 14 cards, k cards are with the cross up
and therefore 14-k cards are with the circle up. In the remaining stack of 9
cards are 14-k cards with a cross up.
Then turn the stack of 14 cards round.
Now there are 14-k cards with a cross up in both stacks.Note that we do not
know exactly how many cards are lying with a cross up in both stacks (or how
many cards are lying with a circle up). We only know that both stacks have
the same number of cards with a cross up.
What's that number? ;)
View Answer & Explanation
Answer
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6
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Explanation
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Looking at the diagram in rows, the central circle equals half the sum of the numbers in the other circles to the left and right of the centre.
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