1. By request of Wiseman.

The Lawn Mower Man

Imagine a lawn mower with a stop/start switch. One click of the switch turns the lawn mower on
the next click turns it off the next click turns it on and so on. Now imagine a person able to turn
it on and off as quickly as necessary.

He turns the mower on, then after exactly 1 minute he turns it off. He turns the mower back on after half a minute then off after another quarter minute.

He repeats this process but always reducing the time interval by exactly half each time. The sum of all these progressively smaller times is exactly two minutes.

The question now comes in 2 parts:

1.) After exactly 2 minutes is the lawn mower switched on or switched off?

2.

3. 1. Indterminate.
2. Indterminate.

Math example: 1-1+1-1+1-1+1-1+...... = ?

4. Agreed with mathman.

Another example:

Sometimes all possible outcomes are considered the answer on a closed interval. In this case, the lawnmower is both on and off!

5. Good try guys, I'll post the correct answer tommorrow.

BTW this is a 2 part puzzle maths + logic

6. Hmm... Are we assuming physical restraints?

7. Originally Posted by halorealm
Hmm... Are we assuming physical restraints?
Nope!

You are required to give the correct answers to part 1 and part 2 to successfully
complete the puzzle. Part 1 maths and Part 2 logic.

8. Okay. Well, the only way I can approach this visually is to graph it.

Take the x-axis, let it represent time in minutes. We'll plot our points on the interval .

For instants the lawnmower is turned on, we'll plot points for . For when it's turned off, we'll plot points on .

Just as the on/off frequency increases, the wave behaves increasingly erratic, where there is no definite limit at the 2 minutes.

So, I still don't understand how the answer would be other than undefined/indeterminate... only making me more eager to see the correct one posted

11. Originally Posted by KALSTER
Pretty much based on it.

12. Chris, you seem not to understand your own "puzzles"

mathman told you the answer - here's another way of looking at it. Suppose we call the "on-to-off" sequence as a 1-cycle, and the sequence "off-to-on-to--off" as a 2-cycle (notice in defining these cycles we are counting the number of "to's")

It should be easy to see that if the number of such cycles is exactly divisible by 2, your machine will be off, and on otherwise.

Question: is infinity exactly divisible by 2 or is it not?

There is some serious math that occurs to me in this connection, but for now I cannot be bothered (hint it has to do with modulo arithmetic)

13. Originally Posted by Guitarist
Chris, you seem not to understand your own "puzzles"

mathman told you the answer - here's another way of looking at it. Suppose we call the "on-to-off" sequence as a 1-cycle, and the sequence "off-to-on-to--off" as a 2-cycle (notice in defining these cycles we are counting the number of "to's")

It should be easy to see that if the number of such cycles is exactly divisible by 2, your machine will be off, and on otherwise.

Question: is infinity exactly divisible by 2 or is it not?

There is some serious math that occurs to me in this connection, but for now I cannot be bothered (hint it has to do with modulo arithmetic)

He was correct with part 1, but this was designed as a 2 part puzzle with second part based on logic.
I've tried several times to hint towards finding the correct answer to part 2, it's not difficult. I would suggest you re-read the puzzle my friend.

14. Originally Posted by Chrisgorlitz
By request of Wiseman.

The Lawn Mower Man

Imagine a lawn mower with a stop/start switch. One click of the switch turns the lawn mower on
the next click turns it off the next click turns it on and so on. Now imagine a person able to turn
it on and off as quickly as necessary.

He turns the mower on, then after exactly 1 minute he turns it off. He turns the mower back on after half a minute then off after another quarter minute.

He repeats this process but always reducing the time interval by exactly half each time. The sum of all these progressively smaller times is exactly two minutes.

The question now comes in 2 parts:

1.) After exactly 2 minutes is the lawn mower switched on or switched off?

If we are talking of a real lawn mover then the switch would not survive an infinity of on/off switching so after two minutes it will be broken (By Murphys law equivalent to an off position) For Idealised Lawn movers there is no defined status since there is no last switching in an infinite series of switching. Which means theres something wrong with the thought experiment.

15. Originally Posted by KALSTER
Whats similar is the infinite halving process. Supposing to prove you cant get from x to y. It can be done in two ways:
1 to get from x to y you have to go half the way, then half of whats left and so on...since there always some part of the distance left you will never reach y. (this is the most common way)
2 to get from x to y you have to go half the way,but to get there you must first come to the half of the way to halfway...then of course there another point at half the way to the half of the halfway... and so on so you cant even begin to move towards y!

16. 1.If there's no physical restraints then theres nothing wrong with either answer. i.e. there isn't enough information to imply or negate either one.
You could have some lawnmowers that end up on after a process like that, and some that end up off.

17. Ok, the correct answer. Remember the puzzle is in 2 parts.

1.) unknown
2.) yes

Explanation:

Part 1.) After exactly 2 minutes is the lawn mower switched on or switched off? Well as I think most of you worked out the answer was: indeterminate/unknown/undifined

Part 2.) If the the the lawn mower had already been switched on to start with would the outcome still be the same? Part 2 is based on logic, the question that needs to be asked
here is does the outcome change by knowing wether the lawn mower was switched on to start with, obviously it doesn't because logic tells us that if we couldn't get a definite answer in part 1 when we knew the lawn mower was switched off to start with then just by knowing the lawn mower was switched on to start with still doesn't give us a definite answer as to wether the lawn mower ends up switched on or off.

Therefore the answer to part 2 has a definite answer which is yes, yes because the outcome is still the same, we still cannot know the final state of the lawn mower.

18. Originally Posted by Chrisgorlitz
Ok, the correct answer. Remember the puzzle is in 2 parts.

1.) unknown
2.) yes

Explanation:

Part 1.) After exactly 2 minutes is the lawn mower switched on or switched off? Well as I think most of you worked out the answer was: indeterminate/unknown/undifined

Part 2.) If the the the lawn mower had already been switched on to start with would the outcome still be the same? Part 2 is based on logic, the question that needs to be asked
here is does the outcome change by knowing wether the lawn mower was switched on to start with, obviously it doesn't because logic tells us that if we couldn't get a definite answer in part 1 when we knew the lawn mower was switched off to start with then just by knowing the lawn mower was switched on to start with still doesn't give us a definite answer as to wether the lawn mower ends up switched on or off.

Therefore the answer to part 2 has a definite answer which is yes, yes because the outcome is still the same, we still cannot know the final state of the lawn mower.
In a way you are playing with words. The answer I gave (indeterminant for both) is essentially the same as your answer. Calling the second answer yes when the first answer is indeterminant is wordplay.

19. I wouldn't call it "wordplay", but mathman was still essentially correct in his first post.

The question was posed in a yes/no manner, so it wasn't exactly the proper way to answer (nonetheless correct).

But, I see Chris was putting a lot of emphasis on the logic part (which everybody else pretty much overlooked) and it seems he's been rightfully consistent throughout the whole thread. Clever question!

20. Originally Posted by mathman
Originally Posted by Chrisgorlitz
Ok, the correct answer. Remember the puzzle is in 2 parts.

1.) unknown
2.) yes

Explanation:

Part 1.) After exactly 2 minutes is the lawn mower switched on or switched off? Well as I think most of you worked out the answer was: indeterminate/unknown/undifined

Part 2.) If the the the lawn mower had already been switched on to start with would the outcome still be the same? Part 2 is based on logic, the question that needs to be asked
here is does the outcome change by knowing wether the lawn mower was switched on to start with, obviously it doesn't because logic tells us that if we couldn't get a definite answer in part 1 when we knew the lawn mower was switched off to start with then just by knowing the lawn mower was switched on to start with still doesn't give us a definite answer as to wether the lawn mower ends up switched on or off.

Therefore the answer to part 2 has a definite answer which is yes, yes because the outcome is still the same, we still cannot know the final state of the lawn mower.
In a way you are playing with words. The answer I gave (indeterminant for both) is essentially the same as your answer. Calling the second answer yes when the first answer is indeterminant is wordplay.
Hi mathman, the idea of the puzzle was mean't to be fun and encourage you all to think in a logical way, I wasn't trying to be perdantic or word play as you call it.
I couldn't understand why you guys all seemed to agree that part 2 was indeterminate, because I designed the puzzle to show that logically if part 1 was indeterminate then part 2 had to be the same which logically gives us a definite answer, even though an extra press on the switch would seem to suggest a different answer.

What it seems is that probarbly in fairness you and the rest of you guys did understand the correct answer but just didn't really read the question properly.
Please again remember though it's only for fun, don't take these puzzles to seriously there are no prizes.

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