Brain Teasers
Shooting Arrows
Paul and James shot 100 arrows, each managing to hit the target 50 times. With the score tied they broke for lunch. After the break, the shooting was not as sharp. Paul shot 89 arrows but only managed to hit the target 13 times. James shot 50 arrows without hitting the target once. Paul claimed that his percentage after the break was better than James', so therefore, he must be the better shot. James naturally disagreed. Who had the better average for the day?
Answer
Neither, they would be tied. Paul took 189 shots and hit the target 63 times, giving him 1/3 in hits. James shot 150 arrows and hit the target 50 times, also giving him 1/3 in hits.Hide Answer Show Answer
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Comments
blaze, where in the puzzle does it say how many arrows James shot in total. it is impossible to calculate an average without the correct information. is this another one of those incomplete and therefore impossible puzzle like the others your so good at eg: "third of six" which belies all logic and reason or your new "light train" which doesn't explain the answer. Please either make sure your submissions are complete or at least have a logical explaination.
Where did 63 come from? It doesn't make any sense at all? James could have shot 500 arrows and not hit any after Paul missed his 89. Then Paul is right, his percentage is better.
Argh!
Argh!
How would you arrive at this answer, given the facts presented? Either one can't, or I'm beginning to slip mental gears.
I got lost even at the start. "Paul and James shot 100 arrows." It doesn't say apiece. That means they each hit the bullseye every time, assuming they shot an equal number before the break. Mad-ade needs to chill out.
Ok, first, 100 arrows and 100hits, that makes a percentage of 100% each for person A and B. then, 50/189 does not equal 1/3. and when it's not saying how many arrows and hits B has after lunch, this puzzle is imposible to solve!
Not enought information to get an answer
I agree that there isn't enough information in the question. But what concerns me more is that this was approved by the editors. How did that happen?
Has this teaser been edited after the comments placed? Sure there is the word "each" missing. They shot 100 arrows (each). I thought that was implied anyway. This teaser is far better than some posted on this probability site which have no information remotely linked to probabilty. I guess I assumed they fired 100 arrows each and I like the teaser because at first sight it looks like the guy who missed all his shots after lunch did worse but their averages were the same . Good One!
It makes sense. trust me. Good One!
Actually, to make things more dramatic, James could have 69/70 the first part (slighty less than 99%) and Paul could have 48/48 (100%). Then, James could hit 3/48 (6.2%), Paul has 10/70 (14%). After combining, much to Paul's chagrin, James wins 72/118 vs. Paul's 58/118.
As you see, I can split a winning proposition into two smaller losing propositions.
As you see, I can split a winning proposition into two smaller losing propositions.
I agree with Jimbo that the word "each" seems to be missing in light of the answer...
However as written (it says that together they shot 100 arrows each hitting the target 50 times)each one of them hit the target 50 times out of 50 shots in the morning. However in the afternoon, James hit the target 0 times out of 50 shots and Paul hit the target 13 times out of 89 shots. Overall, their averages are:
James - 50/100 or 50%
Paul - 63/139 or 45.3%
So James is the clear winner for the day.
However as written (it says that together they shot 100 arrows each hitting the target 50 times)each one of them hit the target 50 times out of 50 shots in the morning. However in the afternoon, James hit the target 0 times out of 50 shots and Paul hit the target 13 times out of 89 shots. Overall, their averages are:
James - 50/100 or 50%
Paul - 63/139 or 45.3%
So James is the clear winner for the day.
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