Mathematical puzzles

[Sharp Nacelle]

Look - I was asked to do it, OK? And I hope this is the best place too.

You have a 5x5 chessboard and a pawn is on a corner square. Using the normal moves of a pawn, what's the highest number of consecutive moves it can make, only visiting each square once. Here's one way to get you going:

http://i55.tinypic.com/30l2nio.jpg
...and so on.

You don't have to use this as your beginning, as long as you begin in a corner and move as a pawn usually does.

[owlart]

That's moving as a Knight, not as a pawn. Pawns only move one square forward (or one square diagonally to take) at a time.

[Sharp Nacelle]

Fuck, you're absolutely right. I meant knight all along. :o

Professor Penrose would be so disappointed in me.

http://i53.tinypic.com/2mcgmc3.jpg

[Rachie]

1354

thats the best i can currently get, however im sure you must be able to do them all.

I HAVE 23 knight moves lol - 2 one direction, 1 the other

[owlart]

This is my solution:

[owlart]

1351

thats the best i can currently get, however im sure you must be able to do them all.

I HAVE 23 knight moves lol - 2 one direction, 1 the other

You need to start in a corner Rachie, that's the rules! :-)

[Sharp Nacelle]

Well done owlart.

Here's my solution:

http://i53.tinypic.com/2u3y4j6.jpg

It's basically a matter of going around in a spiral.

[Sharp Nacelle]

You need to start in a corner Rachie, that's the rules! :-)

I interpreted her diagram as starting in the bottom right corner.

[Sharp Nacelle]

As I say, it's not my puzzle, but that's how I worked it out originally. It was a demonstration by Prof. Roger Penrose that the human mind can easily spot a pattern that a computer can't. He came to my class when I was about 16 and although I was the first to work it out, I'd not bothered to actually write in the numbers. I did manage to convince him that I really had got the solution though.

OK, someone else's turn to set a puzzle?

[owlart]

I interpreted her diagram as starting in the bottom right corner.

Oops, yes, now I look again that's clearly what she did!

[Sharp Nacelle]

OK, here's a quick one:

What's the lowest prime that, when expressed in binary, has an even number of 1s and 0s? For example, 5 is a prime, but it has two 1s and only one 0, so it doesn't count.

[MercilessDomme]

OK, here's a quick one:

What's the lowest prime that, when expressed in binary, has an even number of 1s and 0s? For example, 5 is a prime, but it has two 1s and only one 0, so it doesn't count.
It could be 5 - just write it as 0101

[Sharp Nacelle]

It could be 5 - just write it as 0101

Good point. I'd not thought of leading zeros, but of course any number of leading zeroes could be introduced.

[Rachie]

I thought all binery had to start with a 1?

if so would the answer be 37

13 = 10101
17 = 10001
19 = 10011
23 = 10111
29 = 11101
31 = 11111
37 = 100101


37 = 1 0 0 1 0 1 =
3 lots of 1 and 3 lots of 0

Sorry if im doing it incorrect.

The way i was shown to work out was
have the number has it got any 32s in it yes so use a 1
37 - 32 = 5 (so now use 5)

can you fit 16 in 5 = no so 0 (10)
can you fit 8 in 5 = no so 0 (100)
can you fit 4 in 5 = yes so 1 (1001)

5-4 = 1 so no use 1

can you fit 2 in 1 = no so 0 (10010)
can you fit 1 in 1 = yes so 1 (100101)

Hope done this correct so answer = 37

[Sharp Nacelle]

37 was the number I was thinking of for quite some time. But then I thought 'hang on a minute, what about...?'

[Rachie]

I SUPPOSE YOU COULD COUNT 2 AS PRIME NUMBER = 10 IN BINERY

OTHER THAN THAT YOU HAVE:
3 = 11
5 = 101
7 = 111
11 = 1011
13 = 10101
17 = 10001
19 = 10011
23 = 10111
29 = 11101
31 = 11111
37 = 100101

Cant believe i tried working out every number until 37. Started at 7 as i couldnt imagine it being that simple.

So my answer is 2.
The following one is 37

[Sharp Nacelle]

Yes, I reckon it's 2, and the next is 37 - unless anyone knows different?

Well done Rachie.

Anyone got another puzzle?

[Sharp Nacelle]

Pretty simple one:

A machinist has a 26cm x 26cm square metal plate. He needs to drill 27 evenly-spaced holes on each edge of the plate. How many holes does he drill in total?

[Rachie]

Puzzle pieces are 8mm height x 15mm wide there are exactly 561 pieces in puzzle.

a) How many different combinations of puzzle design are there?
b) What would the area of these puzzle sizes be?
c) How many edges would each puzzle be?
d) If I pick a random piece out of the puzzle what chance is it of being an edge?
e) If my board to do the jigsaw on is – 500mm x 500mm, what chance have I got of doing the jigsaw on here.
f) What area of the board would be left

HAPPY PUZZLING,

[Sharp Nacelle]

Puzzle pieces are 8mm height x 15mm wide there are exactly 561 pieces in puzzle.

a) How many different combinations of puzzle design are there? 6 - 17x33, 11x51, 3x187, 33x17, 51x11, 183x3
b) What would the area of these puzzle sizes be? 67320 sq mm
c) How many edges would each puzzle be? 2 would have 96, 2 would have 120, and 2 would have 376.
d) If I pick a random piece out of the puzzle what chance is it of being an edge? In the 17x33 and 33x17 puzzles it's 1 in 5.843, in the 11 x 51 and 51x11 puzzles it's 1 in 4.675, and in the 3x187 and 187x3 puzzles it's 1 in 1.492
e) If my board to do the jigsaw on is – 500mm x 500mm, what chance have I got of doing the jigsaw on here. 1 in 2
f) What area of the board would be left 182680 sq mm

I'm likely to have several things wrong though...

[Kisune Karnon]

Pretty simple one:

A machinist has a 26cm x 26cm square metal plate. He needs to drill 27 evenly-spaced holes on each edge of the plate. How many holes does he drill in total?

102 holes. definitely simple.

[nina@]

Just a puzzle I found somewhere...

A man who had lived at the highest-numbered address on his street moved to another house on the same street.

He noted that the sum of all the addresses below his new address was the same as the sum of all the addresses above his new address. (Every numbered address on the street is used.)

He had owned some beautiful brass house numbers and was pleased to discover that he did not have to purchase any new ones. For his new house, he used all of the brass numbers from his previous house.

What is his new address?

[qmu]

Thank you nina@, stumbled across this post when I was going to sleep and spent the last one and a half hour on it --' (yep, I have problems). I probably did it in the most convoluted way, but here it is

http://i.imgur.com/YAnBOph.png

[Wordsmiff]

Oh, that kind of pawn?!

[sweet.eater]

102 holes. definitely simple.

But it's ... 104.

[sweet.eater]

How about this? Can anyone solve this?

https://image.ibb.co/bVfRMk/14728_F7_D_C877_4840_A690_A1_AA07057_FF0.jpg

[Runesmith]

I'll admit that I can't, but I could google the answer for it:

How-do-you-find-the-positive-integer-solutions-to-frac-x-y+z-+-frac-y-z+x-+-frac-z-x+y-4 (https://www.quora.com/How-do-you-find-the-positive-integer-solutions-to-frac-x-y+z-+-frac-y-z+x-+-frac-z-x+y-4)