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

2015-01-08

213. Operation 2015

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Given a pair of positive integers a, b, the operation ab is defined as 23 × a + 31 × b.
For example, 20∗15 = 23 × 20 + 31 × 15 = 925.


Determine both pairs of positive integers x, y such that xy = 2015.

2014-12-18

212. Circle shard

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In the diagram is a semicircle (half disk) with radius 5 cm.  The semicircle is divided into five equal arcs, as shown by the ().  Determine the area of the shaded region (coloured region).

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2014-12-15

211. Saline system


There are 6% and 10% saline solutions.  By combining some of each of these solutions, and adding an extra 20 g of water, you want to make 200 g of an 8% saline solution.  Determine how many grams of the 6% and 10% solutions are needed.