The first card “trick” (more of a puzzle, really) was from Marilyn Burns’ blog. It’s called the 1-10 card investigation.
Here is a video of Marilyn Burns introducing the problem.
Some extensions:
- Try using more cards, maybe all 13 in a suit. More?
- Try tucking 2 cards instead of 1. What order will produce the numbers in order.
Then we looked at another card trick from NRICH:
The Trick:
Select any 15 cards from a pack and lay them out on the table - face up - in three equal columns.
Ask someone to choose one card from the 15 and tell you which column it is in.
Collect up the three columns into piles keeping the cards in order. Put the three piles together with the chosen column in the middle.
Now lay out the cards again - face up - in three columns placing one card in each column in turn. Ask the person which column contains the card this time.
Collect up the cards in the same way and lay them out for a third time.
Ask once more which column the card is in - collecting the cards for the third and last time in the same way - with the chosen column in the middle.
Now count down to the middle (8th) card and show it to the person. "Is that your card?"
Our challenge was to figure out why it works and if it works for other numbers than 3 by 5.
Solange and Ray also shared a couple other puzzles and problems:
Strawberry Ice-Cream
A man has three daughters. His friends, who have never met the children, want to know how many years old the daughters are. The man gives them a hint.
Hint # 1
“The product of their ages is 72.”
The friends say this is not enough information so the man gives them a second hint.
Hint # 2
“The sum of their ages is equal to my house number.”
The friends go out and look at his house number and tell the man that they still do not have enough information to determine the ages. The man admits that they need one more clue and gives them a third hint.
Hint # 3
“The oldest of the girls likes strawberry ice-cream.”
Now the friends can determine the ages, and so can you! How old are the three girls?
