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# Maths problem

• Garr - yes I know the first one was a bit easy!  My excuse is that my boys have very kindly given me their cold and my head is full of goo

(plus, these being the not so  bright members of the class, I was looking for really easy solutions, so having to do several steps to get to 3x8 is a bit difficult for them!)

• 8 + 4 - 9 x 3 = 24   should of course have read 8 + 4 - 9 x 8 = 24

Thank  you Barkles.  I will now write out 100 times 'I must not forum without my glasses on'

Do I have to see you after school for punishment too?

• Thanks Stump.  I knew I got it wrong only when I saw the answer.

Fraggle, don't worry, I wasn't saying you should've got it.  There are plenty of times I should've got things but my brain just let's me down at the last moment.  I'll never forget getting 99% in a calculus test because I managed to add 7 and 6 together to get 15!!  If you start looking in the wrong direction with something like that question, you might spend days trying to get the answer.

Do we know the problem below (which I'm not going to name because it'll be too easy for people to pull out the solution)?  It's always a cracker to share with people.

The "XXXXX XXXX" problem

Imagine you're in a game.  There are 3 doors in front of you which you cannot see behind.  There is only you and the quiz host in this game.

Behind 2 doors are coconuts, and behind 1 door is a luxury yacht (they're big doors, ok?).  Now, we'll assume you always want the luxury yacht, just in case there's anyone out there with a bizarre coconut fetish!

You are asked to pick a door.

The quiz host now removes one of the other doors (but he will never take away the luxury yacht because that'd be a pretty naff game).

You are then told you can either stick with the door you have chosen, or you can change to the other door.  Remember, you still can't see what's behind either one.

What should you do?
Should you stick, change, or does it make naff all difference either way?
What are the probabilities each way?

NB - this is a question often used to show how straight forward logic can get the wrong answer and unpleasant, but well formulated maths will prevail, BUT if you are careful with your logic, you'll get it right.

• Barbarella
• I know that one Garr - I was about to post the same problem myself. It's a great example.

TP - that's still not right unless you write (8 + 4 - 9)  x 8 = 24

8 + 4 - 9 x 8 =  is 8 + 4 - 72 = -60

left to right associativity is only true for operators of the same precedence.

• here's another I like because it shows that our gut feeling on conincidence is often wrong

All twenty-five of my students want to invite me to their birthday party. What is the probability that I get at least two invites for the same day?

It's a lot higher than you would guess.

• ah - the Monty Hall problem

choose a different door
• for MH probability goes from 1/3 to 1/2 if you change
• Been a long time since I was at school but don't think you do need the brackets.  If you follow the sum along the line and key it into a calculator as it stands the number at the end is 24.

left to right associativity is only true for operators of the same precedence - Sorry, I have no idea what this means - not only been a long time since school but I was never very good at arithmetic .... that's why I'm an accountant

• TP - multiplication has a higher precedence than addition and subtraction. That measn you have to do it first. You must multiply 9 by 8 before you carry out the adds/subs.

when all the operators have the same precedence you do work from left to right.

and i'm wrong on MH I think - it's goes to 2/3 doesn't it?

• It doesn't work like that on Countdown .... obviously Carol doesn't know this either!  Best you explain it as I'm still a bit confused.
• mellifera speaketh a different tongue
• Is the answer 0.57 Melli, on the assumption no-one's born on 29th Feb?
• I'm going to hace a think about that when I get home Mellifera and come back here tonight probably with the wrong answer.
• Yeah! that's right. BCDB

It's amazing I think

• TP - I am right. On countdown they do the equivalent of what others on this thread did and break the procedure down into separate sums. That is, they use the answers of one sum to feed into the next.
• Whoooo-hooooooooooooooooo!

I was worried that I wouldn't get it right, and I'm a statistician by qualification. Especially since I struggled to get my head round teh switching problem before (it's a Bayesian thing, isn't it?)

• Barkles - you are a headmaster aren't you? Haven't you ever heard of BODMAS?
• Monty Hall is Bayesian.

congrats.

now help me out with the explanation of arithmetic

• Just doing brain test on Facebook, back in a tick ...
• Yes Melli I am, but if I knew what BODMAS meant I'd know if I knew it or not.

• http://en.wikipedia.org/wiki/Order_of_operations

an example very like yours TP is given in the first few lines

(if you find wikipedia more credible than me)

• Brackets, Orders, Division, Multiplication, Addition, Subtraction
• ah right.. yes.

erm....

• Nuts!  I'm struggling to get my formula correct for Mellifera's puzzle!  I've not given up yet.  I'll wait until I have a moment of inspiration, and if it doesn't come in the next 24 hours, I'll give in.  I've seen this problem before, but I just can't remember how to take everything into consideration.
• Mellifera i understand you!

Garr come on!

• Garr - wanna hint?

• Precedence is just a way of avoiding ambiguity in an operation without brackets.

x+n*y ...  how do we know whether the person who wrote that operation means add xn to x then multiply by y; or do they mean multiply y by n then add to x. We know because of precedence. With no brackets we have to do the multiplication first, so it is "multiply n by y then add to x" that is meant.

If, conversely, what the person writing teh operation wants to express is "add n to x then multiply the whole thing by y" then they would have to write:

(x+n)*y ... the addition in the brackets has to be done *before* the multiplication, so we can override precedence with brackets.

Of course in the first example  we could express "multiply n by y then add to x" as:

x+(n*y) ... but the brackets are superfluous, because of the precedence of multiplication over addition. We already know we have to multiply first, so we don't need the brackets to tell us.

Next week, partial differential equations and hyperplanes. Remember to bring your sextants and plumb lines. I'm just off to get a new tank top.

• don't try to take all the things that could happen into consideration, rather consider what couldn't happen.
• RPN is so much easier.