[Prof. Templeton]

Professor Templeton had decided to spend some time at a remote cabin in the Adirondack Mountains in New York. He would get some much needed relaxation, maybe do some fishing, and write up a puzzle that he had been working on some time during the six full days he was to spend there. When the professor awoke in the morning of the first day, he thought to get the write-up out of the way first so he could enjoy the rest of his time unencumbered. The puzzle was already written by hand and only needed to be typed into the computer. When he unpacked his lap-top and started typing, none of the letters that he pressed on the keyboard appeared correctly on the screen. Oh No! The lap-top must have gotten damaged and now the letters were mixed up. The Professor, being a puzzle-minded sort of chap, quickly thought of a solution. He would type in what he had written down, print it, and then retype in what was printed on the page. Eventually the correct words would have to come up. Assuming the 26 letters are mixed up, the professor needs 7 ½ hours of sleep each night and 15 minutes to eat, 3 times per day. The document takes 4 minutes to type for every configuration and ½ a minute to print. Also assume there is no time spent between any activities and no typing can be done while printing (computer runs much too slow). Can the professor be guaranteed to have the correct document printed before leaving first thing on the morning of his seventh day using this method?

This is not a lateral thinking puzzle.

[Guest]

converting it to ASCII and entering it out of the picture <_< ....

and which lake in the Adirondack's?

Edited February 11, 2009 by Dawg

[Guest]

If you discover one letter per typing, then you have plenty of time. It would take 26 tries = 117 min, and you have 1260 retries = 5670 min.

However, if you need to pass over all the combinations (more than 4*10^26), then it's not possible.

So, let's say it's not guaranteed.

EDIT: Wrong maths

Edited February 11, 2009 by Skywalker

[HoustonHokie]

Making a couple of assumptions, I think you'd have plenty of time to type the puzzle and go fishing, even on the first day.

Hopefully, the computer is consistent in the outcomes. For example, if you type "B", you always get "G". And, hopefully, if you type "b", you'll get "g", and not something else. If that's the case, then you can solve the puzzle like this:

Assume what the professor was typing was the alphabet: "ABCDEFGHIJKLMNOPQRSTUVWXYZ." And what he got out was the alphabet shifted by one character: "BCDEFGHIJLKLMNOPQRSTUVWXYZA." Then, when he types in "BCDEFGHIJLKLMNOPQRSTUVWXYZA" he'll get "CDEFGHIJLKLMNOPQRSTUVWXYZAB." After 26 such iterations, "ABCDEFGHIJKLMNOPQRSTUVWXYZ" comes out. Each iteration is 4 + 0.5 = 4.5 minutes, and 26 iterations takes 26*4.5 = 117 minutes. The results are probably not a simple shift like this, but something more like a cryptogram, but the principle is the same in that it will only take 26 iterations to get done, assumping simple (consistent) substitution of one character for another.

So, after almost 2 hours of painful computing on the first morning (followed by another couple painful hours online with the outsourced tech support - typing by cryptogram), the professor will make a quick trip to the nearest shipping location, send the laptop off to be repaired, pick up lunch on the way back, and enjoy the rest of his vacation. Hope the fish are biting and your cell phone breaks, to complete the incommunicado plan - the best vacations are the ones where the office cannot get in touch with you

[Guest]

# of days: 7

Time per day: 24-7.5-.75=15.75 hrs

Total time = 15.75 * 7 * 60 = 6615 minutes

Time / cycle = 4.5 minutes

Total cycles = 6615 / 4.5 = 1470 cycles

So now the question is: is he guaranteed to cycle through in less than 1470 cycles?

[Guest]

Lets assume that all the letters are wrong and also that there are no sections of the alpabet that form a closed loop (e.g. a=b, b=c, c=a). These asumptions are valid considering the puzzle with the idea that after enough iterations of typing the complete message will appear.

While there are 1.5e25 different combinations for the arrangement to be (25!) only 26 iterations maximum will be needed and so it will take less than 2 hours to find it.

So yes the riddle will be typed.

[Guest]

Ok, the way I am looking at it is in terms of closed loops and Lowest Common Multiples. For example, let's say there are two loops in the sequence: one is 3 characters long and the other is 23. The lowest common multiple of 3 and 23 is 3*23=69. Then it would take 69 cycles through the sequence before both loops lined up (much longer than just 26).

I've been playing around and the largest LCM I have found is 1155 (loops of 11, 7, 5, and 3) which is still less than the 1470 cycles available to the professor over the week.

Therefore, I say yes, he will get it, but it may take him the majority of the week.

[Guest]

Assuming all letters point to one other letter that has not been used, and can not point to themselves, there must be between 1 and 13 "letter loops" where all letters point to each other in a circle. The size of these letter loops determines how many iterations are required to guarantee the correct combination is found.

The highest amount of attempts can be represented by the highest product possible of numbers that sum up to 26 and are not factors of eachother, without repeats: 3,5,7,11. The minimum amount of iterations required to guarantee you find the correct combination is 3*5*7*11 = 1,155. This would take 5198 minutes = 87 hours = 5.5 days (15.75 hours per day not sleeping or breaking). He would, at worst, enjoy only half a day of vacation.

[Guest]

@HH: if only it were that simple! I think Voltage and Llam4 have a better representation of the problem and solution.

But who wants to spend the entire vacation typing, when there's fish to be caught? Here's a way to be done by lunchtime:

Type:

qwertyuiop

asdfghjkl

zxcvbnm

then print whatever you end up with.

Put this over your keyboard as a template, and hunt-n-peck to find the proper keys to type the desired letters. It'll take a lot longer than 4 minutes to type the puzzle this way, but surely less than an hour. You might even have time to catch your own lunch.

If Prof T insists on using his method, he can still get some fishing in:

Omit the printing step. Just keep typing in the same document, referencing the lines above instead of a piece of paper. That way the prof can bring his laptop on the boat, and type while waiting for the fish to bite.

Edited February 11, 2009 by Cherry Lane

[Prof. Templeton]

Making a couple of assumptions, I think you'd have plenty of time to type the puzzle and go fishing, even on the first day.

Hopefully, the computer is consistent in the outcomes. For example, if you type "B", you always get "G". And, hopefully, if you type "b", you'll get "g", and not something else. If that's the case, then you can solve the puzzle like this:

Assume what the professor was typing was the alphabet: "ABCDEFGHIJKLMNOPQRSTUVWXYZ." And what he got out was the alphabet shifted by one character: "BCDEFGHIJLKLMNOPQRSTUVWXYZA." Then, when he types in "BCDEFGHIJLKLMNOPQRSTUVWXYZA" he'll get "CDEFGHIJLKLMNOPQRSTUVWXYZAB." After 26 such iterations, "ABCDEFGHIJKLMNOPQRSTUVWXYZ" comes out. Each iteration is 4 + 0.5 = 4.5 minutes, and 26 iterations takes 26*4.5 = 117 minutes. The results are probably not a simple shift like this, but something more like a cryptogram, but the principle is the same in that it will only take 26 iterations to get done, assumping simple (consistent) substitution of one character for another.

So, after almost 2 hours of painful computing on the first morning (followed by another couple painful hours online with the outsourced tech support - typing by cryptogram), the professor will make a quick trip to the nearest shipping location, send the laptop off to be repaired, pick up lunch on the way back, and enjoy the rest of his vacation. Hope the fish are biting and your cell phone breaks, to complete the incommunicado plan - the best vacations are the ones where the office cannot get in touch with you

Ah, but what about loops (see posts below)

1 2 3 4 5 6 7 8 9 Original

4 1 2 3 7 5 6 9 8 What it maps to

3 4 1 2 6 7 5 8 9

2 3 4 1 5 6 7 9 8

1 2 3 4 7 5 6 8 9

4 1 2 3 6 7 5 9 8

3 4 1 2 5 6 7 8 9

2 3 4 1 7 5 6 9 8

1 2 3 4 6 7 5 8 9

4 1 2 3 5 6 7 9 8

3 4 1 2 7 5 6 8 9

2 3 4 1 6 7 5 9 8

1 2 3 4 5 6 7 8 9

Took 12 total because of the loops 1234, 576, 89

# of days: 7

Time per day: 24-7.5-.75=15.75 hrs

Total time = 15.75 * 7 * 60 = 6615 minutes

Time / cycle = 4.5 minutes

Total cycles = 6615 / 4.5 = 1470 cycles

So now the question is: is he guaranteed to cycle through in less than 1470 cycles?

Only six full days are available.

Ok, the way I am looking at it is in terms of closed loops and Lowest Common Multiples. For example, let's say there are two loops in the sequence: one is 3 characters long and the other is 23. The lowest common multiple of 3 and 23 is 3*23=69. Then it would take 69 cycles through the sequence before both loops lined up (much longer than just 26).

I've been playing around and the largest LCM I have found is 1155 (loops of 11, 7, 5, and 3) which is still less than the 1470 cycles available to the professor over the week.

Therefore, I say yes, he will get it, but it may take him the majority of the week.

Is that the largest LCM, what about different loop lengths?

Edited February 11, 2009 by Prof. Templeton

[Prof. Templeton]

@HH: if only it were that simple! I think Voltage and Llam4 have a better representation of the problem and solution.

But who wants to spend the entire vacation typing, when there's fish to be caught? Here's a way to be done by lunchtime:

Type:

qwertyuiop

asdfghjkl

zxcvbnm

then print whatever you end up with.

Put this over your keyboard as a template, and hunt-n-peck to find the proper keys to type the desired letters. It'll take a lot longer than 4 minutes to type the puzzle this way, but surely less than an hour. You might even have time to catch your own lunch.

If Prof T insists on using his method, he can still get some fishing in:

Omit the printing step. Just keep typing in the same document, referencing the lines above instead of a piece of paper. That way the prof can bring his laptop on the boat, and type while waiting for the fish to bite.

Hey now! Stop thinking laterally. It'll get you in trouble.

[Guest]

Hey now! Stop thinking laterally. It'll get you in trouble.

Sorry, can't stop. One more solution:

to the nearest library (not more than an hour from anywhere in Adirondack Park) and use the library computers. Type for four minutes, then drive back to vacationland.

[HoustonHokie]

ok, I see it now. Needed more coffee, I think (that's twice today I've come up with some oddball stuff). I don't see a way to get more than 1155 cycles for the LCM. The only other primes available other than 11, 7, 5, & 3 are 2, 13, 17, 19 & 23, and they don't appear to help much. And if you have 15.75 * 6 * 60 / 4.5 = 1260 cycles available, you've still got time to get the puzzle written. Of course, it'll be a pain in the rear to log in, which continues to cut into the fishing time.

Of course, I think CL has the solution you'll ultimately adopt if you find yourself in that spot. Lateral thinking is just what we do here...

Edited February 11, 2009 by HoustonHokie

[Guest]

Is that the largest LCM, what about different loop lengths?

These numbers represent the different loop lengths. One loop of 3 letters, one loop of 5 letters, one loop of 7 letters and one loop of 11 letters. The worst case scenario would be the last letter in each loop, requiring 3*5*7*11 = 1155 attempts.

[Guest]

I'm with CL

First, find something better to do with your vacation time.

Secondly, do you even have an internet connection that far from civilization? If not, why not wait until you get home to post it and salvage some of your vacation?

[Prof. Templeton]

ok, I see it now. Needed more coffee, I think (that's twice today I've come up with some oddball stuff). I don't see a way to get more than 1155 cycles for the LCM. The only other primes available other than 11, 7, 5, & 3 are 2, 13, 17, 19 & 23, and they don't appear to help much. And if you have 15.75 * 6 * 60 / 4.5 = 1260 cycles available, you've still got time to get the puzzle written. Of course, it'll be a pain in the rear to log in, which continues to cut into the fishing time.

Of course, I think CL has the solution you'll ultimately adopt if you find yourself in that spot. Lateral thinking is just what we do here...

These numbers represent the different loop lengths. One loop of 3 letters, one loop of 5 letters, one loop of 7 letters and one loop of 11 letters. The worst case scenario would be the last letter in each loop, requiring 3*5*7*11 = 1155 attempts.

how about

1,4,5,7,9 what would be the LCM?

[Guest]

how about

1,4,5,7,9 what would be the LCM?

First of all, you can't have a loop of 1 letter. (I assumed a loop constituted more than one letter and no letter pointed to itself, correct me if I'm wrong.)

To have 4,5,7 and 9 you would strand 1 letter that could not be wrong.

[Prof. Templeton]

I'm with CL

First, find something better to do with your vacation time.

Secondly, do you even have an internet connection that far from civilization? If not, why not wait until you get home to post it and salvage some of your vacation?

I have to agree. When I'm on vacation it's all about doing nothing. Don't try to pack my down time full of activities. *glares at wife*

[Prof. Templeton]

First of all, you can't have a loop of 1 letter. (I assumed a loop constituted more than one letter and no letter pointed to itself, correct me if I'm wrong.)

To have 4,5,7 and 9 you would strand 1 letter that could not be wrong.

True. I just threw it in so no one would say "but that doesn't total 26"

[Guest]

True. I just threw it in so no one would say "but that doesn't total 26"

That's the proof. All 26 letters must be used, therefore 4,5,7,9 is not a possible solution because the remainder is 1 and you can not have a loop of 1.

However, 3,5,7,9 would be a possible solution because the remainder is 2, which constitutes a 2-letter loop. Problem there would be the 3 is a factor of 9 meaning the 3 would not be included in the outcome and the product is very low.

So I stand by 3,5,7,11.

Edited February 11, 2009 by Llam4

[Prof. Templeton]

That's the proof. All 26 letters must be used, therefore 4,5,7,9 is not a possible solution because the remainder is 1 and you can not have a loop of 1.

However, 3,5,7,9 would be a possible solution because the remainder is 2, which constitutes a 2-letter loop. Problem there would be the 3 is a factor of 9 meaning the 3 would not be included in the outcome and the product is very low.

So I stand by 3,5,7,11.

no guarantee that 1 letter isn't out of order.

[Guest]

no guarantee that 1 letter isn't out of order.

except the op:

none of the letters that he pressed on the keyboard appeared correctly on the screen

True, we don't know if the Prof pressed ALL the letters to determine this, but I would have, were I faced with that situation.

Edited February 11, 2009 by Cherry Lane

[Prof. Templeton]

except the op:

True, we don't know if the Prof pressed ALL the letters to determine this, but I would have, were I faced with that situation.

Trapped by my own words.

[Guest]

Professor Templeton had decided to spend some time at a remote cabin in the Adirondack Mountains in New York. He would get some much needed relaxation, maybe do some fishing, and write up a puzzle that he had been working on some time during the six full days he was to spend there. When the professor awoke in the morning of the first day, he thought to get the write-up out of the way first so he could enjoy the rest of his time unencumbered. The puzzle was already written by hand and only needed to be typed into the computer. When he unpacked his lap-top and started typing, none of the letters that he pressed on the keyboard appeared correctly on the screen. Oh No! The lap-top must have gotten damaged and now the letters were mixed up. The Professor, being a puzzle-minded sort of chap, quickly thought of a solution. He would type in what he had written down, print it, and then retype in what was printed on the page. Eventually the correct words would have to come up. Assuming the 26 letters are mixed up, the professor needs 7 ½ hours of sleep each night and 15 minutes to eat, 3 times per day. The document takes 4 minutes to type for every configuration and ½ a minute to print. Also assume there is no time spent between any activities and no typing can be done while printing (computer runs much too slow). Can the professor be guaranteed to have the correct document printed before leaving first thing on the morning of his seventh day using this method?

This is not a lateral thinking puzzle.

This is the correct answer!!!

First of all calculate how many cycles he can type:

6 days x ((24 - 7.5) hours/day x 60 minutes/hour - 45 minutes) / (4.5 minutes/cycle) = 1260 cycles

Next calculate the maximum number of cycles he could possibly have to type. In order to do this you have to find the set of numbers with the largest lowest common multiple that have a sum of 26. In this case the set is 1, 4, 5, 7, and 9. So:

1 x 4 x 5 x 7 x 9 = 1260 cycles

Yes you can have a loop of one letter because z=z is a complete loop, and the puzzle didn't say all 26 letters were mixed. Furthermore, the puzzle did say "none of the letters that he pressed on the keyboard appeared correctly on the screen."

Therefore, assuming he has exactly six days to implement his solution, he will have exactly enough time to print the correct document in the worst case senario.

[Guest]

1. Take 26 pieces of tape, plus a piece for any additional punctuation marks, periods, commas, etc.

2. work your way across the keys and put the corresponding tape on each key as you go.

3. After all of the keys are remarked with the new letters, type up the document via the "hunt & peck" method.

How long could it take?

[Prof. Templeton]

This is the correct answer!!!

First of all calculate how many cycles he can type:

6 days x ((24 - 7.5) hours/day x 60 minutes/hour - 45 minutes) / (4.5 minutes/cycle) = 1260 cycles

Next calculate the maximum number of cycles he could possibly have to type. In order to do this you have to find the set of numbers with the largest lowest common multiple that have a sum of 26. In this case the set is 1, 4, 5, 7, and 9. So:

1 x 4 x 5 x 7 x 9 = 1260 cycles

Yes you can have a loop of one letter because z=z is a complete loop, and the puzzle didn't say all 26 letters were mixed. Furthermore, the puzzle did say "none of the letters that he pressed on the keyboard appeared correctly on the screen."

Therefore, assuming he has exactly six days to implement his solution, he will have exactly enough time to print the correct document in the worst case senario.

That was the answer I was going for, but unfortunately I left the OP ambiguous. While it doesn't say that all the keys on the keyboard where pressed, just that all the ones that Prof. T did press where wrong. CL is correct, however, in saying that the wording does lead one to assume that all the keys are mis-matched. So I will twist my own arm and be forced to accept the previous well thought answers and make a promise to be more vigilant in the future. *wishes I had bn's magic edit wand* Regardless, the answer to the question is the same

Yes. It can be guaranteed that it was typed in time.