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Test Republic dice puzzle (Zagorski Software Tester)

On May 30, 2013, in Syndicated, by Association for Software Testing
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Test Republic gave this interesting problem at their Facebook page:
“””
Recently, during the evaluation of a Online Casino Game, one of our consultants was asked this mathematical puzzle, before he was hired to consult.


“A solo dice game is played where, on each turn, a normal pair of dice is rolled. The score is calculated by taking the product, rather than the sum, of the two numbers shown on the dice. On a particular game, the score for the second roll is five more than the score for the first; the score for the third roll is six less than that of the second; the score for the fourth roll is eleven more than that of the third; and the score for the fifth roll is eight less than that of the fourth. What was the score for each of these five throws?”
“””
Here is the solution.

Answer
10,15,9,20,12

Reasoning
There is 21 combinations of dice products without repetition: (javascript code). Add this for this problem:
disp(pick(2, [], 0, [“1”, “2”, “3”,”4″,”5″,”6″], true) + ” combos”); 

1, 2, 3, 4, 5, 6
4, 6, 8, 10, 12
9, 12, 15, 18
16, 20, 24
25, 30
36

Eliminating duplicate products we have 18 unique products.

1, 2, 3, 5
4, 6, 8, 10
9, 12, 15, 18
16, 20, 24
25, 30
36

Using given data: __ +5 __ -6 __ +11 __ -8 __ we start our elimination.
+5 eliminates 36, 30, 24, 16, 18, 12, 9, 8, 6, 2
because adding 5 will not gives are number which is valid dice game product result.
So we have following possible first results: 25, 20, 15, 10, 4, 5, 3, 1
When we add + 5 we can eliminate (same reasoning applies): 1
And we have following possible second result: 30, 25, 20, 15, 9, 10, 8
-6 eliminates following products : 25, 20, 9
So we have possible third results: 24, 9, 4, 2
+11 eliminates: 24, 2
So we have  possible fourth result: 20, 15
And finally -8 eliminates 15 so we have only one fifth result: 12
Going backwards we can calculate all results:
Fifth: 12
Fourth: 20
Third: 9
Second: 15
First: 10

Why is this testing puzzle? Because for tester is important to have elimination skills. Yes, for this problem you need to have math knowledge, but elimination reasoning is what is important. It is not possible to test everything, you need to know how to eliminate and test only what is important.

 

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