#56 Diffy squares
Diffy is a subtraction game. You choose four whole numbers between 1 and 12 and write them on the corners of a square. Then, you find the difference between numbers at neighbouring corners and write the answer at the midpoint (see above).
Join the midpoint numbers to form a diamond, then repeat the process until you end with four zeroes in a square (which always happens, eventually). In the example, there are five squares, but with the right starting numbers you can get more than five. Your challenge is to find whole numbers between 1 and 12 that will do this.
鈥� You are a high achiever if you get more than six Diffy squares.
鈥� You are a genius if you get 10 Diffy squares.
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#55 Ton up
The four parts that you divide 100 into can be worked out as follows:
100 = A + B + C + D = (M 鈥� 4) + (M + 4) + (M / 4) + (M 脳 4) for some value of M.
You could rewrite that as 100 = M + M + 录M + 4M = 6录M, so 400 = 25M or M = 16.
Therefore, the four parts are 12, 20, 4 and 64.
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Quick quiz #48
1 Which white crystalline solid with the chemical formula C10H8 is associated with the characteristic smell of mothballs?
2 In differential calculus, velocity is the first derivative of displacement with respect to time, and acceleration the second. What is the third?
3 Adipose tissue is an orotund way of describing which feature of our bodies?
4 The bacterium Bordetella pertussis is responsible for which respiratory infection that is especially common in young children?
5 In the northern climes of Canada, where would you be if you had wandered into a muskeg?
Answers below
Quick quiz #48
Answers
1 Naphthalene
2 Jerk, or the rate of change of acceleration with time
3 Fat
4 Whooping cough
5 In a marsh or bog