Estimable reader: Appended to problem 42 is a dialogue highlighting an unsettling outcome of a limited (and limiting) approach to mathematics education.

2015-03-28

229. Pulley system



In the diagram are three pulleys, A, B and C, connected with belts.  A’s radius is 1 cm, B’s larger radius is 3 cm and smaller radius is ½ cm, and C’s radius is 2 cm.  Also, B’s larger and smaller wheels have the same axis and move together.

⒜  When pulley A rotates once, determine the distance that the belt connected to A moves.
⒝  When pulley A rotates once, determine how much pulley B has rotated.
⒞* When pulley A rotates once, determine how much pulley C has rotated.

2015-03-24

228. Square-in-triangle

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In the diagram, right △ABC contains square GHIJ.  Determine the ratio of the area of square GHIJ to the area of △JIC.

(from Twitter)

2015-03-22

227. Black & white card game

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There are many black cards and white cards in a bag.  In the following games, take one card at a time out of the bag and arrange the cards in a row.

Game 1.  When 2 cards of the same colour occur consecutively, the game is finished.  If the game is not finished even after arranging the 6th card, but is finished after arranging the 7th card, determine how many arrangements of cards from the 1st card to the 7th card are possible.
Game 2*.  When 3 cards of the same colour occur consecutively, the game is finished.  If the game is not finished even after arranging the 6th card, but is finished after arranging the 7th card, determine how many arrangements of cards from the 1st card to the 7th card are possible.