Brain Teasers ? or 50 Years On........... ?

yes, that is what i had in mind for the Pythagorean approach -- you're a mathtype expert now !

the proof with vector manipulation is somewhat less "painful", as follows:

hope you like it as much as i did...

enjoy

ken

The UK Lottery is now based on selecting 6 numbers from 59.

The probability of winning is now............................?

It's been a long time, but I'll rush in with 6!/(59 x 58 x 57 x 55 x 54 x 53)

I think you have a typo in here: 6!/(59 x 58 x 57 x 56 x 55 x 54) looks better to me .

My own approach was 6/59 * 5/58 * 4/57 * 3/56 * 2/55 * 1/54 = 0,00000002219, which is just the same.

Spot-on JRH. (with Mulbery's edit)

If you invert it you get an equally difficult probability to grasp viz 1 in 45,057,474

Which as MDS states in another thread, is about the same as the chances of being struck by lightening.

I'm not sure that's strictly true, but it's in a similar ball-park (or Parish)

If you've been playing the same numbers every week (from 1 to 49), if you keep doing so, will you have less chance of hitting the jackpot than somebody that randomly picks from the new range of numbers (1 to 59)?

Oops...yeah...the typo. Thanks for spotting that.

 I have a "gut" feeling that you are right.

Deliberately choosing 6 from 49 when the machine is picking 6 from 59 suggests you are denying yourself a big chunk of possibility. But......................

...............are you ?

Any single set of six numbers has the same possibility of coming up as any other. Your odds of winning don't change if you choose all new numbers each time,  if you pick from a subset, or if you play the same numbers each time, which is the ultimate subset.

Balls !!!!

Ok, i'm basically on holiday, or rather putting finishing touches to a new home. A busy day but now able to relax. I didn't bring my A-Level maths books with me............. but I thought that a simple problem might keep a few newbies occupied for a few minutes, preferably with their own brain in gear, but I appreciate trawling the internet is the way of the world these days.............

I have 12 spheres (think ball-bearings) that LOOK identical. But one, and only one of them is either heavier or lighter than the others.

I have a pair of scales (think the Scales of Justice) on which I can place any number of spheres to compare their weights, e.g. three on each side - and if they balance, then none of these six is the "odd one out". Such an event would be classed as "a single weighing"

What is the minimum number of weighings I need to perform to identify the "Odd Ball" and determine whether it is light or heavy ?

Obviously a description of the sequence of weighings is required to accompany the answer........

Adam is prohibited, because his method is too clever !!!!

A simple brain tease.

1  3  5

2  4  ?

Ok, somebody has to start...............!

Rationality says "its obviously 6 !"

Wisdom says, "that's far too obvious, even though its a 'simple ' brain tease !"

So we eliminate "6"

Pi

Correct. It's not "6". Think laterally.

With the most obvious answer out of the way, how about "5"? My train of thought: 1+4=5 (V-pattern), 2+3=5 (inverted V).

Is is automotive related?

Correct.

Yep, that's the one. Thinking  outside the (gear)box

Ah, one of these. At least I can point to my cars 6-speed gearbox as a cheap excuse .

Drove up to the downs for a walk this morning, to give Steve's teaser a bit of thought.

Drove back more convinced than ever that the answer was going to be "6"

Subject should be obvious, but the answer shocked me !

50,000

£25,500

92

71

11%

£6.50

Assume 6 weeks plus public holidays

SJ and others can advise and use more accurate numbers where appropriate.

Junior doctors hourly pay after their 11% rise

well-spotted, Close.

Try the arithmetic.:-

Deduct the 11% proposed increase.

Use 92 hours

Assume 6 weeks plus public holidays

The £6.50 is the current minimum wage

Try it again with 71 hours and the proposed new starting salary - and although it moves to the right side of the minimum wage, even the living wage begins to look attractive !!

Interesting. Things don't change much over the years. When I was a junior doctor starting out in 1979 I worked out my hourly rate. I used to have two evenings off a week and every other weekend off, all other time was spent in the hospital. My hourly rate of pay was less than 20p an hour. 

Queue the Monty Python sketch. 

I imagine Junior Doctors get a bit of time-and-a-half and possibly even double-time for unsociable hours, but even so, these figures are surprising !