Difference Between Offline and Online Casino

Dated: 27 Jan 2012
Posted by admin
Categoiry: Gambling Tricks
0 Comments

David Sklansky has been given detention for calling his sixth grade teacher a “moron”.  As he’s walking down the hall that night (after taking a face from the ancient gallery), he notices there’s 100 closed but unlocked lockers along one wall. On his first trip down the hall he opens all 100 lockers.  He then goes back to the beginning and closes every second locker. On his third time down the hall, he stops at every third locker and opens it if it’s closed, and closes it if it’s open(call this ‘toggling’). He continues this, toggling every Nth locker on his Nth trip, until on his 100th time down the hall he toggles only the last locker(and no, he doesn’t take anything from the lockers; they’re all empty).

a.)  At this point, how many lockers are open?

b.)  Starting from the first trip, how many toggles are done?

c.)  Which locker gets toggled the most times?

Answer 1:

To be open, a locker must have been toggled an odd number of times.  The number of times locker number N is toggled equals the number of positive integer factors of N.  Since the only natural numbers that have an odd number of factors are the perfect squares, then lockers 1, 4, 9, 16, 25, …. 100 (a total of 10 lockers) are open. Add the total number of factors of the numbers 1 through 100.  My computer gives 482. A tie between lockers 60, 72, 84, 90, and 96.  Each of these got toggled 12 times.  (If we assume that the each trip along the lockers is in a direction opposite to the previous, then locker number N on the first pass would be number M on the return trip, where N+M=101.  A locker would be toggled once for every ODD factor of N and once for every EVEN factor of M.  For example, locker number 5 (N=5, M=96) would get toggled during trips 1 and 5, and during return trips 2, 4, 6, 8, 12, 16, 24, 32, 48, and 96.  Locker numbers 21 and 45 tie with number 5 for the most number of toggles: 12.  There would be a total of 482 toggles. The number of lockers open would be 24.)

Answer 2:

David makes 100 trips down a hall way opening and closing locker doors, but the sixth grade teacher is the moron?

Answer 3:

I’m no great mathematician it’s been years but here goes, if I’m way off base please let me know.
a:10 doors open Depending upon my understanding of what a toggle being correct
b: 482 toggles
c: five lockers are toggled 11 times 60,72,84,90,96

Tags: , , , , , , , , , , ,

Leave a Reply