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Solutions for Act III Scene 2 - Bowling

The puzzle provides a valid ten-pin bowling scoresheet (as suggested by the title) for ten players. A reasonable idea would be to calculate the final score for each player.

Now, taking the first letter of each name spells out ARITHMETIC. Indeed, a strike (X) looks like a multiplication symbol, a spare (/) looks like a division symbol, while a gutter ball (-) looks like a subtraction symbol. Using these interpretations, we can see that each row gives a valid arithmetic expression. Evaluating each expression (obeying the usual order of operations) gives us an integer each time, which suggests that we are indeed on the right idea.

 Name    Bowling score
Arithmetic expression
 Alice  128  62 x 9 - 279/62 x 2/9 - 5/1 = 552
 Rikku  120  35 x 16 x 27 - 6 x 6/9 - 51 = 15065
 Isaac  127  9/27 x 36 - 3 x 7/24 x 8/7 = 11
 Tyrol  115  8/24 x 33 x 9/3 - 15 x 2/3 = 23
 Henri  98  22162/7 - 26 x 4/13 x 23 = 2982
 Masud  108  6/33 x 4235 - 8 x 1/11 x 44 = 738
 Ellis  133  71 x 637/7 - 18 x ((4/3)/3)/8 = 6460
 Tania  85  341/11 x 7/17 - 39/51 - 2 = 10
 Itzel  126  31 x 357 - 7/81 x 54 x 6/4 = 11060
 Craig  111  173/8 - 9/7 - ((456/336)/4)/1 = 20

The next step is found by looking at the names again (the oddness of some of the names would suggest that first letters are not the only piece of information contained within them). Indeed, taking the last letter of each name spells out EUCLIDSALG. This is referring to the Euclidean Algorithm, which is a method for calculating the Greatest Common Divisor of two integers. This implies that we should calculate the GCD of the two integers that we have produced in each row. Indeed, each GCD is no greater than 26, so we can convert these values to letters.

 Name    Bowling score
Arithmetic expression
GCD
 Letter
 Alice  128  552  8  H
 Rikku  120  15065  5  E
 Isaac  127  11  1  A
 Tyrol  115  23  23  W
 Henri  98  2982  14  N
 Masud  108  738  18  R
 Ellis  133  6460  19  S
 Tania  85  10  5  E
 Itzel  126  11060  14  N
 Craig  111  20  1  A

Finally, if we arrange the letters by decreasing bowling score, we get SHANEWARNE (a famous Australian bowler, although in a different sport).
The answer is: shanewarne