Generate newspaper page number sets

Question

A newspaper is made of several sheets; for the purposes of this question, each sheet of newsprint holds four pages of the final newspaper. Here is an example of three sheets of newsprint making up a newspaper with twelve pages:

 ___________
|2    |   11|
|  ___|_____|_
| |4    |    9|
|_|  ___|_____|_
  | |6    |    7|
  |_|     |     |
    |     |     |
    |_____|_____|

(Pages 1, 3, 5, 8, 10 and 12 are on the reverse of these sheets so you can't see them here.)

Your challenge, should you choose to accept it, is to output all the sets of pages that are on each sheet of a given newspaper.

You can take either the number of sheets (which is always a positive integer) or the number of pages (which is always a positive multiple of 4), but please indicate which.

You can output the sets of pages in any reasonable order, as long as it is clear which pages belong in which set.

For example, given an input of 3 sheets or 12 pages, you could output (1, 2, 11, 12), (3, 4, 9, 10) and (5, 6, 7, 8); or you could output (8, 5, 7, 6), (10, 3, 9, 4) and (12, 1, 11, 2); or any variant thereof, but you cannot of course output 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.

This is code golf, so please make your program or function as short as possible. (I will even accept the shortest overall program as the answer on request of its author if doing so will earn me a Winter Bash hat.)

Answer 1

convey, 34 bytes

}
/1:`%""{
^1"v4!<
+"+v}+1
^<","-}

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Pushes n and n+1 to the right per loop.

For each value outputs i and i-pages+1.

Whenever the left loop passes through the top part, output a newline /}. Allow n to pass the loop only pages % 4 times.

Answer 2

J, 18 bytes

Takes number of sheets as input

_4>:\2/:@(,|.)@#i.

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_4>:\2/:@(,|.)@#i.
                i.  0…n: 0 1 2
     2         #    repeat each 2 times: 0 0 1 1 2 2
         (,|.)@     append its rotated version: 0 0 1 1 2 2 2 2 1 1 0 0
      /:@           get the indices to sort: 0 1 10 11 2 3 8 9 4 5 6 7
_4  \               group by 4: 0 1 10 11, 2 3 8 9, 4 5 6 7
  >:                and increment: 1 2 11 12, 3 4 9 10, 5 6 7 8

Answer 3

Husk, 9 bytes

←½Sz+↔C2ḣ

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Argument is the number of pages.

        ḣ   # list of all the page numbers 1..input
      C2    # split into groups of two
  S         # hook: S(fgx) means f(x,g(x))
   z        # zip together
    +       # by combining elements from both lists
            # x = the list of groups of two)
     ↔      # and itself reversed
←½          # now take just the first half of this list
            # of lists of 4-pages per sheet

Answer 4

Perl 5 -n, 38 bytes

$,=$";say$.++,$.++,$_--,$_--while$_>$.

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Takes the number of pages as input

Answer 5

APL (Dyalog Extended), ¹⁶ 14 bytes

¯1 4⍴⍋2/,∘⌽⍨…⎕

Try it online!, Stax

A port of xash's solution.

a full program which returns a matrix.

-2 bytes from Bubbler.

Answer 6

R, 48 bytes

function(N)split(rbind(x<-1:N,N:1)[x],(x-1)%/%4)

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Takes input as the number of pages.

R, 51 bytes

function(N)split(1:(4*N),c(x<-rep(1:N,e=2),rev(x)))

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Takes input as number of sheets.

Answer 7

Scala, 37 bytes

p=>1.to(p/2)zip p.to(p/2,-1)grouped 2

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Returns an iterator of 2-element vectors, each containing a 2-tuple of page numbers opposite each other.

Answer 8

Python 2, 46 bytes

def f(n,i=2):i>n>_;print~-i,i,n-1,n;f(n-2,i+2)

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Takes the number of pages n as input.

A function that prints and terminates with error. If we avoid errors, many different ways to structure the code come out very close.

50 bytes: Try it online!

i=n=input()
while i*2>n:i-=2;print-~i,i+2,n+~i,n-i

50 bytes: Try it online!

n=input()
i=1
while i<n:print-~i,i,n-1,n;i+=2;n-=2

51 bytes: Try it online!

n=input()
i=1
while i*2<n:print-~i,i,n-i,n-i+1;i+=2

51 bytes: Try it online!

f=lambda n,i=1:n/i*[0]and[(i,i+1,n-1,n)]+f(n-2,i+2)

51 bytes: Try it online!

lambda n:[(i,i+1,n-i,n-i+1)for i in range(1,n/2,2)]

Answer 9

K (oK), 21 19 bytes

-2 bytes thanks to coltim

 {1+0N 4#<x,|x:&x#2}

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A port of xash's J solution - please upvote it too!

Answer 10

Jelly, 7 bytes

ḶạÞH‘s4

A monadic Link accepting the number of pages (four times the number of sheets) which yields a list of lists of the page numbers belonging to each sheet.

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How?

ḶạÞH‘s4 - Link: integer, P   e.g.  12
Ḷ       - lowered range (P)        [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11]
   H    - halve (P)                6
  Þ     - sort by:
 ạ      -   absolute difference  ( [ 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5] )   
        -                       -> [ 6, 5, 7, 4, 8, 3, 9, 2,10, 1,11, 0]
    ‘   - increment                [ 7, 6, 8, 5, 9, 4,10, 3,11, 2,12, 1]
      4 - four                     4
     s  - split into chunks        [[7,6,8,5],[9,4,10,3],[11,2,12,1]]

Answer 11

AWK, 46 43 bytes

x=$1{for(;y<x;)$++v=++y","++y","x--","x--}1

Takes the number of pages.

x=$1{

Set x to the number of pages. That will always evaluate to true given the rules, so the block of code will always run.

     for(;y<x;)

Loop until the forward page counter x is larger then the backwards page counter y. It's effectively looping once for every 4 pages, since x and y both change by 2 each time through the loop.

               $++v=++y","++y","x--","x--

Set positional argument v (incremented before it's used) to the next set of 4 pages, adjusting the forward and backwards counters as they are used.

                                         }

Ends the code block.

                                          1

An unconditionally true test with no defined code block causes the default action, which is to print all the positional arguments joined by the OFS variable. The default for that is a space.

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Answer 12

JavaScript (ES6), 47 bytes

f=(n,N=1)=>N<n?[[N,N+1,n-1,n],...f(n-2,N+2)]:[]

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Answer 13

Ruby 2.7, 43 bytes

->n{((1..n/2)%2).map{|v|[v,v+1,n-v,n-v+1]}}

No TIO link, as TIO supports an older version of Ruby.

---

Ruby, 45 bytes

f=->n,k=1{k<n ?[[k,k+1,n-1,n]]+f[n-2,k+2]:[]}

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Answer 14

C (gcc), 72 70 bytes

• -2 bytes thanks to ceilingcat

Takes the number of physical pages.

I compute the last page and then loop through each physical page, getting the distance from the bounds for each one starting from the last page (the middle page numbers).

f(n,i,j){for(i=n*4;n--;)printf("%d/%d/%d/%d ",j+1,i-j,++j,i-j,j=n*2);}

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Answer 15

05AB1E, 7 bytes

Input is the number of pages, output is in a different order, both the pages on each sheet and the sheets.

Lι€Âøιн

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          # implicit input                          8
L         # push the range [1..input]               [1, 2, 3, 4, 5, 6, 7, 8]
 ι        # uninterleave, push [a[0::2],a[1::2]]    [[1, 3, 5, 7], [2, 4, 6, 8]]
  €Â      # duplicate and reverse each list         [[7, 5, 3, 1], [1, 3, 5, 7], [8, 6, 4, 2], [2, 4, 6, 8]]
    ø     # transpose the list of lists             [[7, 1, 8, 2], [5, 3, 6, 4], [3, 5, 4, 6], [1, 7, 2, 8]]
     ι    # uninterleave                            [[[7, 1, 8, 2], [3, 5, 4, 6]], [[5, 3, 6, 4], [1, 7, 2, 8]]]
      н   # take the first element                  [[7, 1, 8, 2], [3, 5, 4, 6]]

---

05AB1E, 8 bytes

Takes the number of pages as an input. Output is in the natural order.

Lι€Âø€{Ù

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          # implicit input                          8
L         # push the range [1..input]               [1, 2, 3, 4, 5, 6, 7, 8]
 ι        # uninterleave, push [a[0::2],a[1::2]]    [[1, 3, 5, 7], [2, 4, 6, 8]]
  €Â      # duplicate and reverse each list         [[7, 5, 3, 1], [1, 3, 5, 7], [8, 6, 4, 2], [2, 4, 6, 8]]
    ø     # transpose the list of lists             [[7, 1, 8, 2], [5, 3, 6, 4], [3, 5, 4, 6], [1, 7, 2, 8]]
     €{   # sort each list                          [[1, 2, 7, 8], [3, 4, 5, 6], [3, 4, 5, 6], [1, 2, 7, 8]]
       Ù  # uniquify the list of lists              [[1, 2, 7, 8], [3, 4, 5, 6]]

Answer 16

Charcoal, 17 14 bytes

Thanks to Neil for -3 bytes!

ＩＥ⪪…⁰⊘θ²⁺⊕ι⁻θι

Try it online! Link is to verbose version of code.

Input is (now) the number of pages.

Explanation

Ｉ               Cast to string
  Ｅ             Map (forEach)
    ⪪    ²       Split on 2 (split into slices of length 2)
     …⁰          Range from 0...
       ⊘θ        ...to half of first input (θ)
          ⁺⊕ι    Add (concatenate) ι (current item, which is the slice), with every element incremented...
             ⁻θι ...to first input (θ) minus the slice (ι)

Answer 17

PowerShell, 56 52 49 bytes

-4 bytes thanks to Neil!
-3 bytes thanks to mazzy!

Takes input as the number of pages:

param($x)for(;$x-$y){++$y,++$y,$x--,$x---join","}

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Answer 18

Vyxal Ṁ, 14 13 bytes

ƛd›D⁰4*ε:›^›W

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Answer 19

Bash, 42 bytes

-1 bytes from @pxeger

for((x=$1;x>y;)){ echo {,}$[++y]\ $[x--];}

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I'm usually the Zsh guy, but here Bash wins by a few bytes because it evaluates brace expansion before parameter expansion:

echo {,}{$[++y],$[x--]}
echo $[++y] $[x--] $[++y] $[x--]

Answer 20

Jelly, 8 bytes

Żx2m0Ụs4

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Another port of xash’s answer, drop that an upvote as well

How it works

Żx2m0Ụs4 - Main link. Takes n on the left
Ż        - [0,1,2,...,n]
 x2      - [0, 0, 1, 1, 2, 2, ..., n, n]
   m0    - Append its reverse
     Ụ   - Grade up; sort the indices by values
      s4 - Split into runs of 4

Answer 21

05AB1E,  10  9 bytes

-1 thanks to ovs!

LΣ<I;α}4ô

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Port of my Jelly answer. Input is the number of pages (four times the number of sheets).

LΣ<I;α}4ô
L         - range
 Σ   }    - sort by:
  <       -   decrement
   I      -   push input
    ;     -   halve
     α    -   absolute difference
       4  - push four
        ô - split into chunks

Answer 22

05AB1E, 20 11 bytes

L2ô2ä`Rδ«Å\

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-9 thanks to @ovs