Safe Cracking
by Dan Meyer
skips
questions
Act One
 1.
What's a number you know is too high?
 2.
What's a number you know is too low?
Act Two
 3.
What information is important here?
 Teacher noteIt seems like there are three important quantities here:
 How long it takes him to write down one fournumber combo.
 How long it takes him to test one fournumber combo.
 How long it takes him to cross off one fournumber combo.
You can have students collect their own data by timing the video and by seeing how fast it takes them to write down / cross off a few fourdigit numbers.
Then you need to know what the final combination is. A close look at the video reveals "8020," but feel free to let your students make that determination.
Act Three
 Teacher noteSo he writes down numbers 00009999. (Seems like a waste of time. What if the combo was "0000?")
He tests out numbers 00008020.
I assume:
 Write a fourdigit number down: 1 second.
 Try it out and cross it off: 4 second.
Total time to write them down: 1 sec/number * (9999  0 + 1) numbers = 10,000 seconds.
Total time to try them out and cross them off: 4 sec/number * (8020  0 + 1) numbers = 32,084 seconds.
Total is 42,084 seconds or 701 minutes or 11.68 hours, which is a lot less time than I would have thought. Assuming he could do that for a couple hours per night without going crazy, and he'd be done in a week!
Sequel
show 62 more questions

Why would anyone bother to write out all of the fourdigit numbers to crack a safe? And then crossing each of them off? Seriously?




Why doesn't the safe have a safeguard that locks you out after some number of attempts? How many different numbers does he have to try?






How long would it take to break a 4 digit lock given it accepts multiple attempts









How long between each attempt? Or can he make multiple attempts in a row?
















How many combinations are there? Assuming the correct combination is the last one you try, how long will it take to try them all?







What's a reasonable expectation for how long it would take to enter a 4digit code?



















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