Last week's Lenny Conundrum didn't quite add up

[okamotosan18]

Okay, now, I have no clue how they figured that it was such a small number of days for 91,584,000 combinations. He could only work like 5,760 of the combos a day, right? 4 tries a minute, 60 mins/hr, 24hrs/day. The answer should have been 15,900 days to finish trying all of them. To get to the answer they say is correct, you go ((60*4 + 60*3)/5,760)*2 which equals 4,575. But that isn't nearly all of the combonations possible. They only calculate for all of the combonations all left and all right.

You have to calculate for all of the different combinations of left/right turning because the little thief didn't know how it was set up.

60<-60<-60 60*60*60=216,000
60->60<-60 "
60<-60->60 "
60->60->60 "
60<-60<-60<-60 60*60*60*60=12,960,000
60<-60<-60->60 "
60<-60->60<-60 "
60->60<-60<-60 "
60->60<-60->60 "
60->60->60<-60 "
60->60->60->60 "


And since they didn't specify if the lock was a high-tech combo lock that would reset if you tried to open it with the wrong combo, you would have to assume that you would have to try all 4-digits combos seperatly from 3-digit combos because they have told us everything that is definite. Ex. You wouldn't be able to try 1->2->3->4 by turning to 4 right after you try the 3-digit combo. Since they go for all possible combos, you would have to try them serperatly as 1->2->3 and 1->2->3->4.

If they wanted us to assume you would only be turning it left or right for one whole combo, they had to actually say that because you can't leave loose ends in a math problem. They told us that we would need to find all possible combos, and that he didn't know the left/right turning system. They need to hire some mathematicians. Hey, maybe that's what I could use my BS in math for

[digitel_anime_fan_20]

I'll have to agree, I'm doing math this year that has to do with such kind of things, you know, the number is an even 3 digit number less than 400, when the digits can repeat, whats the number of diff combinations...You get the point. :/

You have to take into mind EVERY COMBINATION. Neo needs a math tutor... >_<

[WaylonJSmithers]

Yeah, but combo locks don't work that way. They always alternate left and right for each number in the combo.

[okamotosan18]

I think I remember one that was used for like a small home safe that had to turn, push it in like a button and then turn to the next number. And it was like left left right I think

[matchbow]

Hey, I got 2550 days somehow

[hiddenneggs]

It's not possible for the combination to be all left turning or all right turning -- if it were, you could unlock it just by spinning it awhile in one direction or the other.

Combination locks alternate spinning direction -- right to such & such, then left to such & such, then right to such & such.

For a 3-number combination of 60 choices (0-59), there are 60 * 60 * 60 possibilies for the numbers. Double that because we don't know which direction we start with. (For example, if the numbers are 5-32-0, it could be "left to 5, right to 32, left to 0" or "right to 5, left to 32, right to 0.")

For a 4-number combo, it's 60 * 60 * 60 * 60. Again, double the result.

Add those together, multiply by 15 seconds for the time it takes to try each possibility, divide by 60 (60 seconds per minute), divide by 60 again (60 minutes per hour), divide by 24 (24 hours per day), and you get 4575, no rounding required.

[okamotosan18]

Like I said 2 posts ago, we weren't told that we couldn't click the number into place and keep turning. Which means we have to add all those combos on too

[Dag]

I think it was a little bit of preknown knowledge and common sense. But I also see where you are coming from okamo, They should have specified that for those who didnt know.

[cyleigh]

We also weren't told that it wasn't already unlocked and so didn't need to try anything.

I'm sorry, but you are wrong. The method described above is what I used and I too have a Math Degree (with Honours).

[okamotosan18]

It wouldn't matter if it was unlocked, he would've probably gotten the correct combo way before he finished, that wasn't the point. I get problems right if they're set up properly. You couldn't just ask what the limit of f(x)=5x^2 + 1/2(x). Then when they try to guess and you say it was 5 1/2, of course! It doesn't make sense because you weren't given all the information. If you gave that problem to 90,000,000 people, of course a few people would guess that they wanted the limit as x approaches 1. Doesn't mean that because a few people answered it correctly that they set it up properly.

[Mokona]

I wasn't sure if the numbers could be repeated for a combination, and they didn't specify if 3 digit meant 111 or 1 12 1... They really need to specify the problem better.....

All of my friends gave me different answers, sadly none of them were correct None of them know how a vault works so we weren't sure if it was combination or permutation to use :/ Stupid TNT!!!

[hiddenneggs]

Like I said 2 posts ago, we weren't told that we couldn't click the number into place and keep turning. Which means we have to add all those combos on too

No. It was a combination lock, and we were expected to apply real-world knowledge of how combination locks where you turn the dial work.

If you didn't know how those sorts of locks work, you may have made wrong assumptions and therefore included too many possibilities. But that isn't Neopets' fault.

(And as I said in my post, some thought would have demonstrated why one can't keep turning in one direction to unlock a combination lock. It would be useless, since once a thief started spinning the wheel, it would quickly go to each number. It has to alternate directions.)

Mokona, the question didn't refer to "3 digit," it said 3 or 4 numbers; we already knew those numbers were in the range 0-59.

With puzzles of the kind used in the Conundrums, it can be tricky knowing where to apply common-sense understandings and where to think "outside of the box." That's part of the game. (In the current one, for example, you need to be able to "translate" the raw numbers/numerals in a particular, non-mathematical way, see the mathematical pattern that can be derived from those translations, and apply it.)

Granted, I would like it if Neopets would include the explanation along with the answer on completed Lenny Conundrums.

[Stijn]

Haha, that wouldn't surprise me if last week's Conundrum didn't have the correct answer.

I tried to figure it out, and I just received the neomail saying I won. Something MUST be wrong then.

[okamotosan18]

Like I said 2 posts ago, we weren't told that we couldn't click the number into place and keep turning. Which means we have to add all those combos on too

No. It was a combination lock, and we were expected to apply real-world knowledge of how combination locks where you turn the dial work.

If you didn't know how those sorts of locks work, you may have made wrong assumptions and therefore included too many possibilities. But that isn't Neopets' fault....

I guess I wasn't very clear, I didn't say the lock was just turn to a number, then the next. You turn to the number, push it in to click the number into place, then turn to the next one, left or right depending on the combo. Why would a bank use a simple combination lock? I was using real-world knowledge in thinking a bank would want to make the combination as hard as possible to guess. I know how the simple little ones for lockers work, but that wasn't what we were asked to do. And it didn't say to assume anything else. What it did imply was that we had to find all possible combinations not all probable combinations.

[hiddenneggs]

Ah, but with word problems (as opposed to being presented with a straight-out equation) one almost always has to make assumptions.

And we both did. You and I both assumed -- correctly -- that the numbers in the combination were whole numbers. Why? On an implicit basis (say, from the point of view of an alien who somehow knows our language and number system, without knowing anything about our culture), the numbers could very well have been pi, 58.957813549875264516821685158555555, 12.66 repeating, and the square root of 1000. We weren't told that the numbers had to be rational, much less whole, just that they had to be from 0 to 59, but you still understood that that did not mean we had to add all those combos into the mix; otherwise, your total number of possibilities would have been far larger. (Infinite, even.)

Again, then, it isn't about whether to make assumptions, it's which ones to make and which ones to reject -- which ones will allow you to solve it as it's meant to be solved, and which ones will lead you down the garden path. Where to draw the line.