Tuesday, October 31, 2006

Mathematical Card Tricks

Here is a mathematical card trick taken from "Mathematics Magic and Mystery" by Martin Gardner (Dover books, pp 7):

A spectator shuffles the deck and places it on the table. The magician writes down the name of a card on a piece of paper and places it face down without letting anyone see it.

12 cards are dealt on the table, face down. The spectator is asked to touch any four. The touched cards are turned face up. The remaining cards are gathered and returned to the bottom of the deck. Assume that the picked 4 cards are 3,6,10 and a King. The magician states that he will deal cards on top of each four in the following way.

If the card is 10 or any court card, do not deal anything on them.
If the card is not the above, deal a number of cards till they count to 10. For instance, if the card is 3, deal 7 cards by counting: 4,5,6,7,8,9,10. if the card is a 6, deal 4 cards counting: 7,8,9,10.

The values of the original 4 cards are added. In this case 3+6+10+10=29. The spectator is handed the pack and asked to count to the 29th card from the top. This card is turned over. The magician reads his prediction and discovers it the chosen card.

Using only sec 1 algebra, can you figure out how this is done?

Monday, October 16, 2006

Math cartoons for lessons

Here is a cartoon website where you can find an entire list of cartoons ranging in various subjects. Under the "M" section, you have find many math related cartoons that can be used in lessons. However, most of these cartoons are not related to any particular math topic, so there is a need to be selective.

The link is:

Friday, October 13, 2006

A challenging secondary school Geometry problem

Let ABC be an isoceles triagnel with equal angles 80 degress at B anc C. Cevians BD and CE divide angles at B and C into 60+20 and 30+50 degrees respectively. Find Angle EDB.

geometry problem Posted by Picasa

What color is the bear?

A hunter walks 1 mile south. He then turns left and walks 1 mile east, then turns left again and walks 1 mile north. He ends up back where he started and spots a bear. What color is the bear?

The answer is white, as he is at the north pole. What do you see in this question?
As the hunter walks 1 mile south , 1 mile east and 1 mile north, he has formed 2 right angles. But yet he was back at the same spot as he started. This means the triangle formed from the hunter's path contains 2 right angle.

Why is this possible?