Quick! Before the girls come in!

Probability Level 2

While Sage was swimming, Ron steals his clothes and hides them in the Girls' Changing room! Ron puts it in one of 9 lockers, each locker is secured with a lock that requires a 3-digit password.

What is the maximum number of tries required for Sage to find his clothes?

Image credit: Harry Potter and the Deathly Hallows Part 2, Warner Bros


The answer is 9000.

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Yan Yau Cheng by Yan Yau Cheng , 20, Hong Kong

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3 solutions

Aditya Raut
Jun 5, 2014

The code can be any number from 0 \color{#3D99F6}{\Huge{0}} to 999 \color{#BA33D6}{\Huge{999}}

So there are 1000 numbers for a lock. And hence P o o r \Huge{\color{#D61F06}{Poor}} S a g e \Huge{\color{#69047E}{Sage}} has to try 9000 \boxed{\Huge{9000}} times :P

R o n \color{#3D99F6}{Ron} has no doubt done a G r e a t \Huge{\color{#624F41}{Great}} Job and very good Mr. Ron ! That might be a R e v e g e \color{orangered}{Revege} and it has succeeded ! Congratulations .... T h e . . . g i r l \color{orangered}{The... girl} will come in very shortly hopefully !

22 Helpful 0 Interesting 0 Brilliant 0 Confused

But how will sage get to know that his clothes are in girls changing room?

Yash Dev - 7 years ago

he must try his locker first so it's 9001

light yagami - 7 years ago

Damn, HAHAHA. i didn't included "000" HAHAHA I got it wrong :/

Jerico Cayl Samson - 7 years ago

it's revenge* :/

mathh mathh - 6 years, 10 months ago

does anyone know why @Yan Yau Cheng put a picture of ron and hermione about-to-kiss in a problem like this?

A Former Brilliant Member - 3 years, 8 months ago
Bernardo Sulzbach
Jun 22, 2014

Being picky: FIND clothes doesn't imply GETTING the clothes, right?

After 8000 attempts we will have FOUND his clothes (as we are supposing he already knows that they are in the Girls' Changing Room).

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Well well ! @Bernardo Sulzbach , tomorrow you'll come and say he has no need to check any locker, he has FOUND his clothes and they're in "girl's changing room" ! He has found their location though he hasn't got the clothes :P @Finn Hulse @Yan Yau Cheng

Aditya Raut - 6 years, 11 months ago

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Hehe. :D :D

Finn Hulse - 6 years, 11 months ago

I seriously like your idea. =D

But I insist that Sage needs 8000 (maximum) to FIND his clothes supposing he knows that they are in the Girls' Changing room.

This is a frequent kind of problem with word problems in combinatorics, and it gets even worse for ESL guys.

Bernardo Sulzbach - 6 years, 11 months ago

@Finn Hulse Please, comment on this.

Bernardo Sulzbach - 6 years, 11 months ago

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Yeah I think you're right. It's a little confusing.

Finn Hulse - 6 years, 11 months ago

Technically, you're right. Because if you've tried eight lockers with all possible combinations for the locks and you don't get the clothing, you can already make the assumption that the clothes are in the locker you haven't checked yet given your conditions. The question should have asked, "What is the maximum number of tries required for Sage to GET his clothes?"

tytan le nguyen - 6 years, 5 months ago

The number of ways you can form a three digit number is 10 * 10 * 10 = 1000. 1000 * 9 = 9000 (For nine lockers) . So according to math the solution is 9000.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

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