A quick maths question

[tomparryharry]

Hi Folks,

 

Here's a quick question for you.

 

I'm running an 8 wagon shunting puzzle. How many permutations of the 8 wagons can I make? Is it 8, to the power of 8, or is it 8, to the power of 7?

 

Cheers!

 

Ian

[34theletterbetweenB&D]

8! (eight factorial, 8x7x6x5x4x3x2).

[Steve K]

8! (eight factorial, 8x7x6x5x4x3x2).

 

Indeed, unless there's some cunning scheme that the OP is intending to employ.

 

To clarify for the benefit of non-mathematicians, if you have 8 wagons, and space only for those 8 wagons, then the first wagon you place on the puzzle can go in any one of those 8 spaces, the second can go in any one of the remaining 7, the 3rd has a choice of 6, and so on. Hence the correct answer, as above.

[tomparryharry]

Cheers!

 

That gives me 40,320 permutations, give or take a wagon or two....

 

Ian

[jcm@gwr]

Pedant mode on-

I'm not sure that is correct, in a normal Inglenook

you have 8 wagons, but 11 spaces (assuming it

is the normal 5-3-3) and you are only trying to

sort 5 of the wagons into the correct order on the

longest siding. The other 3 wagons are irrelevant

to the puzzle, either way the permutations could

be more (if you include all the places you can put

the wagons) or less if you are only interested in

the completion of the puzzle!

Pedant mode off

 

(Either way, it's a lot!)

[Steve K]

Hmm... so if it's 8 wagons in 11 spaces, should the answer be 8!, or 11!/3!*, or something else?

 

 

*I think this is how many ways you can fit 8 wagons in 11 spaces (adds up to 6,652,800), assuming that you don't mind where the 3 gaps are...

[kevinlms]

Another maths question.

 

 

If a customer owes me a sum of money and the debt is going off to a debt collector for recovery. Now if the DC takes 35% on successfully recovering the funds, how much must I add to the original debt, to cover that 35%, so I receive the original amount?

 

TIA

[dhjgreen]

Another maths question.

 

 

If a customer owes me a sum of money and the debt is going off to a debt collector for recovery. Now if the DC takes 35% on successfully recovering the funds, how much must I add to the original debt, to cover that 35%, so I receive the original amount?

 

TIA

100/65*debt

[kevinlms]

100/65*debt

Thank you.

[NorthBrit]

Another maths question.

 

 

If a customer owes me a sum of money and the debt is going off to a debt collector for recovery. Now if the DC takes 35% on successfully recovering the funds, how much must I add to the original debt, to cover that 35%, so I receive the original amount?

 

TIA

If  the DC is the 'Heavy Mob'  add as much you like.  LOL

[jcm@gwr]

Hmm... so if it's 8 wagons in 11 spaces, should the answer be 8!, or 11!/3!*, or something else?

 

 

*I think this is how many ways you can fit 8 wagons in 11 spaces (adds up to 6,652,800), assuming that you don't mind where the 3 gaps are...

 

But, does it really matter?

 

Surely the point is to enjoy the puzzle and/or the shunting.

[Lightspice]

Indeed, unless there's some cunning scheme that the OP is intending to employ.

 

To clarify for the benefit of non-mathematicians, if you have 8 wagons, and space only for those 8 wagons, then the first wagon you place on the puzzle can go in any one of those 8 spaces, the second can go in any one of the remaining 7, the 3rd has a choice of 6, and so on. Hence the correct answer, as above.

Agree with this, but assuming you have some way of turning the wagons around (turntable or loop) you could have an awful lot more!

[royaloak]

Another maths question.

 

 

If a customer owes me a sum of money and the debt is going off to a debt collector for recovery. Now if the DC takes 35% on successfully recovering the funds, how much must I add to the original debt, to cover that 35%, so I receive the original amount?

 

TIA

I thought they recovered your debt in full plus whatever they have added on as an increasing rolling amount to cover their costs and time, so you get your full debt back and they get however much depending on how long and whatever else they have had to expend on recovering your debt.

[Pacific231G]

Cheers!

 

That gives me 40,320 permutations, give or take a wagon or two....

 

Ian

Hi Ian

That's true for the total number of permutations of 8 wagons and no spaces (How many ways can you arrange 8 wagons in a siding say) but for Alan Wright's classic 5:3:3 Inglenook  where the challenge is to make up a 5 wagon train in a particular order from a total of 8 wagons in the yard the permutations are 8!/(8-5)! which is 6720.

For a shunting puzzle though it's not so much the total number of final permuations that make it challenging but the number of ways of getting to that with the aim being to do it in the smallest number of moves. 

 

There's a good explanation of all this from Adrian Wymann here http://www.wymann.info/ShuntingPuzzles/shunting-puzzles.html

 

Of course, if you have a shunting puzzle that is not Inglenook or Timesaver do tell us more. They're the two classic ones but there are others and quite possibly others still that are yet to be invented.