While out bowling with his friends, a man managed to throw eight strikes (all ten pins knocked down in a
single throw) and not a single gutterball during the entire game. To his amazement, his final score was
only 99 points! Assuming there were no penalties or fouls, can you come up with a ten frame scorecard
with eight strikes and a final score of only 99 points?
HOW TO KEEP SCORE IN BOWLING
There are ten pins and ten individual frames in a game of bowling. In each frame you have two throws to
try to knock down all ten pins. Each frame ends with one of three possible results:
1. STRIKE: If you knock down all ten pins in the first throw of a frame, you get a strike. Your score in
the frame in which you bowled the strike will be ten points plus the sum of the pins knocked down on
your next two throws (you'll have to wait until you've thrown two more times to come back and enter the
score in the frame).
2. SPARE: If you knock down all ten pins using both shots of a frame, you get a spare. Your score in the
frame in which you bowled a spare will be ten points plus the sum of the pins knocked down on your next
throw (you'll have to wait until you've thrown one more time to come back and enter the score in the
frame).
3. OPEN FRAME. If you do not knock down all ten pins using both throws of your frame, you have an open
frame. Your score in the open frame is the number of pins knocked down.
In the tenth and final frame, you are still awarded extra throws if you bowl a strike or a spare. If
you bowl a strike (on the first throw), you get
two more throws. If you bowl a spare (on the
second throw), you get
one more throw. If you bowl an open frame, you do not get any additional
throws and the score for the tenth frame is the total number of pins knocked down.
Below is a sample scoresheet. X's represent strikes and /'s represent spares.
Just to illustrate how scoring works, let's look at the first two frames.
FRAME 1: The X symbol indicates that a strike was bowled. The score (recorded in the lower half of the
scoresheet) for the first frame is therefore ten plus the sum of the pins knocked down on the next two
throws which in the example are nine and one (the first two throws of the second frame). The / symbol
for the second throw in frame two indicates a spare which means that all remaining pins were knocked
down in the second throw. Nine pins were knocked down on the first throw so one pin was knocked down on
the second throw. The score for the first frame is 10 + 9 + 1 = 20.
FRAME 2: Remember, the scores in the lower half of the scoresheet are cumulative so the score (recorded
in the lower half of the scoresheet) for the second frame will be 20 (the cumulative score from the
previous frame) plus whatever is scored in the second frame. Since a spare was bowled in the second
frame, the score for that frame is ten plus the sum of the pins knocked down on the next throw which in
the example is five (the first throw of the third frame). So the score for the second frame is 10 + 5 =
15 and the cumulative score (recorded in the lower half of the scoresheet) is 20 (the cumulative score
from the previous frame) + 15 = 35.
So, back to the question... Assuming there were no penalties or fouls, can you come up with a ten frame
scoresheet with eight strikes and a final score of only 99 points?