Question 1152465: A typical die has the numbers 1 to 6 arranged on its sides so that the sum of each pair of numbers on opposite sides is equal. What is the greatest product of two numbers on opposite sides?
Answer by ikleyn(52798)   (Show Source):
You can put this solution on YOUR website! .
So, the pairs of numbers in opposite sides are (1,6), (2,5), (3,4).
The number of pairs to check is so few ( only 3, actually ) that the quickest way is to multiply the numbers in pairs
and then compare, to get the ANSWER in this way, which is 12.
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Another way is to notice that the sum of numbers on opposite sides is always 7;
then to write the quadratic function q(n) = n*(7-n) and to find its maximum for integer values n from 1 to 6, inclusive.
If you want, you may go this way, but calculating three products and comparing the results is much faster.
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