A Contest For You...A Dare!
Try these problems from an old AtlanticPacific Mathematics League contest? This particular version was aimed at students in grades 59. You have 30 minutes to complete all six questions.
 A strip of paper 1 cm wide by 50 cms long is marked off at intervals of 1 cm in order to cut off a series of 1 cm squares. In seconds, how long will it take to cut the 50 square cms if each cut takes 4/5 of a second and the paper must not be folded?
 The sum of a set of 12 numbers is 186. If each of the numbers is tripled and 4 is then subtracted from each product, what is the sum of the new set of 12 numbers?
 It is understood that (x)(y) means the product of a and y. If (1)(2)(3)(4)(5)(6)(A)(B)(C)(10)(11) = N, then in terms of N find the value of (12)(11)(10)(C)(B)(A)(6)(5).
 If 4x + 2(7x) = 6, then find the value of x/3 + 3.
 If the average of two numbers is AB and one of the numbers is A, then what is the other number?
 A cube of ice, 2 ft to an edge and weighing 456 lbs, is left sitting in the hot sun. After several hours, while it is still a cube, it only measures 1 ft to an edge. How much weight has it lost?
Source: AtlanticPacific Mathematics League, April 10, 1985
Hint: It's a contest...no hints allowed! Plus, time is passing...
Solution Commentary: Rather than provide solutions, I will provide only some comments:
 To create 50 squares, how many cuts are needed?
 In each case you have 3y4, twelve times...so, using the dristibutive property...
 (3)(4) = 12...thus...
 Some straight forward algebra...little thinking unfortunately.
 What fraction of its volume has been lost...can you determine this visually?
