[jazzship]

Emily can click a mouse ten times in 10 seconds. Buzzy can click a mouse twenty times in 20 seconds. Anthony can click a mouse five times in 5 seconds. Assume that the timing period begins with the first mouse click and ends with the final click. Which one of these computer users would be the first to complete forty clicks?

"It's Anthony. The actual period is 1 second less than the time given. Emily completes ten clicks in 9 seconds. Buzzy completes twenty clicks in 19 seconds. Anthony completes five clicks in 4 seconds. This gives us the approximate rates: Anthony 1.25 clicks/second Emily: 1.1 clicks/second, Buzzy 1.05 clicks /second.

The answer makes no sense to me. Explanation?

[Guest]

If you make some assumptions, I think it's Buzzy, but not for the reasons given so far. Also, there IS a way it can be Anthony.

There's no reason to assume a consistent amount of time between clicks.

For example, Anthony may make his first click (clock starts), then clicks three more times in the next 1/10th of a second (really fast), then waits. Just as the clock strikes 5 seconds, he clicks for the fifth and last time. This satisfies the description. He then starts again until reaching 40 clicks.

Similarly for Buzzy, he hits click number 20 when the clock hits 20 seconds. That's what we know from the description.

There are assumptions that I think give Buzzy the victory. There is a non-zero amount of recovery time between the final click that stops Anthony's clock at 5 seconds, and his sixth click. Also, assume the recovery time is the same for all users. For Anthony the recovery will happen 7 times, but for Buzzy only once.

If you don't count the recovery time, all users are equal. However, if Anthony recovers 10 times faster than Buzzy, he would win.

What am I missing?

[Guest]

It depends on the phase and period of each clicker.

These values can vary depending on interpretation of the problem.

There exists a set of inequalities that dictate what phases and periods are allowed for each player.

Depending on what values for these you assume, any of the players can win.

Typically language doesn't this much room for interpretation, as we just go with what would be implied in the most common case from experience.

However the answer provided by the original question departs from this common understanding and opens up the door to an infinite number of interpretations (one for each set of assignments of the phase and periods of the clickers).

In some of these assignments, Anthony wins, in some Emily wins, and in some Buzzy wins.

Everyone who has provided an answer has assumed one such assignment. But is any one assignment the correct answer?

In my opinion the correct answer is one that covers the most possibilities correctly.

[Guest]

Emily can click a mouse ten times in 10 seconds. Buzzy can click a mouse twenty times in 20 seconds. Anthony can click a mouse five times in 5 seconds. Assume that the timing period begins with the first mouse click and ends with the final click. Which one of these computer users would be the first to complete forty clicks?

"It's Anthony. The actual period is 1 second less than the time given. Emily completes ten clicks in 9 seconds. Buzzy completes twenty clicks in 19 seconds. Anthony completes five clicks in 4 seconds. This gives us the approximate rates: Anthony 1.25 clicks/second Emily: 1.1 clicks/second, Buzzy 1.05 clicks /second.

The answer makes no sense to me. Explanation?

When they are on their second click, the time is on one second

[Guest]

when t=0, clicks=1,

when t=4, clicks =5, giving the rate of 1.25clicks per second.

At t=5, Anthony is beginning his second round of 5 clicks in 5 seconds.

after every multiple of t=4, Anthony gets in an extra click (.25 x4).

1.25 clicks/sec x ? seconds = 40 clicks

?seconds = 40clicks / 1.25 clicks = 32 seconds. Anthony wins.