How to Play the Numbers Game


The numbers game is played as follows

The contestant selects six numbers from a choice of twenty-four. These twenty four are grouped into large and small numbers. There are four large numbers (25,50,75 and 100) and the rest are small numbers, two each of one to ten. The contestant selects how many large numbers to have from none to four. Traditionally one large number and five small numbers gives the best chance of solving the puzzle in time.

A three digit number is then generated from one hundred to nine hundred and ninety nine. Contestants have thirty seconds to make the target using the six numbers with the addition, subtraction, multiplication or division operator. If the target cannot be achieved exactly, points are awarded for the closest within a range of ten.
Each number can only be used, unless it appears twice in the selection when it can be used twice. Only integers can be used at any stage of the calculation, and no other mathmatical operators, such as exponents, can be used.

Not all games are mathematically possible.


For example, numbers are 100,3,2,9,4,3 and the target is 309.

Valid answers are
100*3 = 300, 300 + 9 = 309
100+3 = 103, 103*3 = 309 - The 3 can be used twice as it appears twice
100+2 = 102, 102/3 = 34, 34*9 = 306, 306 +3 = 309

Invalid answers are
100 * 3 = 300, 303 + 3 + 6 = 9. There is no 6 in the selection.
100 / 3 = 33.33, 4-3 = 1, 33.33 + 1 = 34.33, 34.33 *9 = 309. All calculation must include whole numbers.
100 * 3 = 300, 300 + 1 + 4 + 4 = 309. 4 has been used twice, but only appears once in the selection.

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