Following macdonjo3 's post, here 's a few I remember A) Difficulty: Easy. How much is: 999*998*997*996*...*-996*-997*-998*-999 No calculators B) Difficulty: Hard. I 've let the number of lockers low so you can bruteforce the result in case the result inspires you to find the analytical solution There are 20 closed numbered lockers and 20 numbered people (1,2,3...). The person with number 1 goes and opens all 20 lockers. After he finishes, the person with number 2 goes through lockers 2,4,6,8,10,12,14,16,18,20 and closes them. After he finishes, the person with number 3 goes through lockers 3,6,9,12,15,18 and if one is open, he closes it, if it is closed he opens it. Similarly for person number 4 etc. How many lockers will still be open after the 20th person has finished? Wanted: The result and a formula for 1 billion lockers and people Please only PM me your answers so that people have the chance to think about it instead of just reading the answers. Winners so far (sorted alphabetically) healzer ionica21 JFoulds Junkfood00 qrazy phracktl SmartMan tacopalypse 45415 Congratulations to all!