An Easy One This Week

Remy wants to buy a car for C pounds, but he only has x < C pounds. He decides to play a gambling game in the hopes of raising his money to C pounds. The rules are as follows:

Remy chooses how much to pay, then n fair dice are thrown. If the sum is even then he gets double his money back, if it is odd he gets nothing. He can play as many times as he likes.

Remy bets all his money if he has less than half of C, otherwise he bets enough to make his total up to exactly C if he wins.

Determine f(x), the probability that he reaches C before going bankrupt.

James Miles : 03 Mar 2010 19:48 |  Tags: Gambit Gambling Mathematics Probability Remy Wednesday Maths |  Comments (0) |  Close comments |  Report a problem

Suzie–Post–Uni You're Doing It WRONG!

Suzie finishes uni and gets a job in a post room at a TV company, hoping she will be promoted to a film producer within a few years.

One day, talking about her ambitions to an assistant-director he tells her that in big companies people don’t so much get promoted as “fail-upwards”.

She decides therefore to deliver the post as badly as possible so that no-one gets their post to the right box, but so that everyone does at least get someone else’s post (to show to everyone how well she is failing).

Given that there are n postboxes and every person gets one batch of post every day:

1.) How many ways can the post be delivered so everyone gets their own post?

2.) How many ways can the post be delivered so no-one gets their own post?

3.) How many ways can the post be delivered so that exactly x (non-specific) people get their own post?

James Miles : 17 Feb 2010 18:24 |  Tags: Michael J Fox Suzie Post Uni Wednesday Maths |  Comments (0) |  Close comments |  Report a problem

Campsite Parties Are Always INTENSE

A company produces 2m long deluxe tentpoles from three rods: one 1m long and two 0.5m long.

The factory builds each rod correct to the nearest 2cm, with even distribution in error. The poles are then welded together from one randomly-chosen long rod and two randomly-chosen short rods.

Another company builds padded cases to hold the tentpoles. It builds cases 201cm long, correct to the nearest 1cm, with even distribution in error.

Each company ships 1,000,000 of its completed product to your control centre to match them up and send on to retailers. Assuming you have perfectly accurate measuring and matching technology:

1a. Would you expect to have any tentpoles and cases left over?

1b. If so, how many? If not, why not?

2. Is there any stage of production where your utility as an expert measurer-matcher could be optimised?

James Miles : 25 Feb 2009 18:18 |  Tags: Accuracy Error Measuring Tentpoles Wednesday Maths |  Comments (0) |  Close comments |  Report a problem

HADOOOUKEN!

In Street Fighter IV, players control their character using an eight-way direction and six buttons¹.

A fireball is performed by pressing down, down-towards, towards+any punch.

How many such special moves can be performed using three combinations of inputs, as in the fireball motion?

^{[1] directions:{up, up-towards, towards, down-towards, down, down-back, back, up-back}; buttons:{light punch, medium punch, heavy punch, light kick, medium kick, heavy kick}}

James Miles : 19 Nov 2008 22:26 |  Tags: Arcade Stick Hadoken Inputs Street Fighter Wednesday Maths |  Comments (0) |  Close comments |  Report a problem

Wednesday Maths Problems, #43: Choco NOM NOM NOM Leibniz

#43
Choco NOM NOM NOM Leibniz

Given an n by m rectangle of Dairy Milk, what is the maximum and minimum number of snaps required to break the bar into nm single squares?

Where a “snap” is defined as a breakage along one line on a solid piece. (So no doubling up of multiple pieces or half snaps, thank you very much.)

James Miles : 29 Oct 2008 20:50 |  Tags: Bar Snap Choco Leibniz Chocolate Dairy Milk Leibniz Mathematics Wednesday Maths |  Comments (11) |  Close comments |  Report a problem

Wednesday Maths Problems, #41 and #42

#41
When the Sun Shines We’ll Shine Together

Check out this picture from Gerard Way’s Umbrella Academy:

It motivates a simple problem:

Find a way of connecting 1, 5, 22, 132, 7, and 72.

The more ingenious the better, especially if order is preserved.

#42
Can You [20] Dig It?

Does there exist a 20-digit positive square integer starting with 11 ones?

BONUS

James Miles : 22 Oct 2008 10:00 |  Tags: Connections Mathematics Number Theory Umbrella Academy Wednesday Maths |  Comments (6) |  Close comments |  Report a problem

Wednesday Maths Problems, #39 and #40

This week, a couple inspired by conversations at work last week. One easy problem and one harder.

#39:
Clink and You’ll Miss It

Bo meets with eight colleagues after work for drinks. Wahey!

The nine people all clink glasses with each other, one-to-one.

How many clinks in total?

#40:
Saturday Night’s Alright for Fighting I MEAN CROSSWORDS

P and everyone in her family can solve a quarter of the clues in a crossword, working alone.

One weekend they each attempt the “Saturday Supergrid” in their own copies of the paper and pool answers at supper to see how much of the puzzle they have solved between them.

Given that their collaborated grid has 1562 clues filled in out of 2048, how many people are in P’s family?

BONUS:

Check out the Wednesday Maths ‘SUPPLEMENTAL’ that was posted on Monday.

James Miles : 15 Oct 2008 10:00 |  Tags: Clink Clink And Youll Miss IT Collaboration Crosswords Elton John Family Glasses Mathematics Wednesday Maths |  Comments (4) |  Close comments |  Report a problem

Wednesday Maths Problems: SUPPLEMENTAL

I thought that Question 1 of last Saturday Times Books’ Two Brains puzzles had an obvious answer, but it turned out not to be the one given. I feel both answers are equally valid but on reflection my answer is one that only someone with a mathematical background would immediately see. What do you think the two solutions are? Which is more obvious to you?

Question 2 was trivial, but then I’m a film geek. Can you do that one too?

James Miles : 13 Oct 2008 18:39 |  Tags: Mathematics Raymond Keene Saturday Times Supplemental Two Brains |  Comments (3) |  Close comments |  Report a problem

Wednesday Maths Problems, #38: A Show With Everything But Yul Brynner

In Duo-Chess, players take two moves at a time.

Professor Qazmickle builds a machine that he claims can always force a win in Duo-Chess, so long as it plays black.

When he tells me this I say unto him that it’s bawsacks.

Why?

(Now answered in the comments, so be careful if you want to work it out for yourself!)

CHRIS JOHNSON BONUS:

Not a Wednesday Maths Problem… ...but this: http://www.youtube.com/watch?v=8HE9OQ4FnkQ

James Miles : 08 Oct 2008 19:40 |  Tags: Chess Force Win Machine Mathematics Puzzle Wednesday Maths |  Comments (1) |  Close comments |  Report a problem

Wednesday Maths Problems, #37: Just Another MySpace Alfie

A young chap lives in London. He has two girlfriends: one in Cambridge and one in Oxford. He sees them often but can never decide whom he likes more, so just lets chance decide where he visits, turning up at London train station and taking the first train to either Cambridge or Oxford. Trains to Cambridge arrive every 30 minutes at platform 1, and to Oxford a couple of metres away on platform 2, also every 30 minutes (though they never arrive at the exact same time). For some reason our wag finds that he sees the Oxford girl much more than the Cambridge one. About nine times out of ten he will visit the girl in Oxford, in fact.

Can you think of a good reason this might be?

(Now answered in the comments, so be careful if you want to work it out for yourself!)

And here’s a joke to go with the problem.

BONUS:

“London train station” just out of shot, aheheh.

James Miles : 01 Oct 2008 09:11 |  Tags: Alfie Mathematics Puzzle Times Trains Wednesday Maths |  Comments (6) |  Close comments |  Report a problem