Draw the combinations that add up to 100

Question

You have a box with a single digit number in each corner:

1|2
---
3|4

If we concatenate the digits along rows left to right, we get 12 and 34. If we concatenate the digits along columns top to bottom, we get 13 and 24. If we add all of these numbers, we get 12+34+13+24 = 83.

Challenge

Write a program to print all such boxes where the sum calculated as above is equal to 100.

Assuming each corner contains a single digit number between 1 and 9, there are 9 combinations: 1157, 1247, 1337, 1427, 1517, 2138, 2228, 2318, and 3119. (Note that there are 25 combinations if we include 0, but we're not for this challenge.)

Note that the example 1234 doesn't work since 12+34+13+24 does not equal 100.

Input

None

Output

Answer boxes in the following format:

A|B
---
C|D

Output should be printed to STDOUT or closest alternative.

Rules

• AB + CD + AC + BD = 100
• Each corner will contain the positive integers 1-9 only.
• 0 is excluded.
• Numbers can be used more than once.
• You need to draw the boxes, as above. (A|B\n---\nC|D\n)
• You need to output all valid answers.
• An additional trailing newline is fine.
• code-golf, so shortest code in bytes wins.
• Standard loopholes and T&C's apply.

This is my first submission so please do let me know if I need to clarify anything.

Answer 1

Pyth, 42 38 34 bytes

V^ST4IqC\ds*VNsM^,T1 2Xj\|N3"
---

The trailing newline in the code is important. The main reason I'm competitive is because I use the vector dot product of [1, 1, 5, 7] and [20, 11, 11, 2] and compare it to 100.

Answer 2

Ruby, 71

As hardcoding is not disallowed (and in any case it is difficult to draw a line) here's a partial hardcoded answer.

1.upto(3){|i|1.upto(7-i*2){|j|print i,?|,j,'
---
',8-j-2*i,?|,i+6,'
'}}

Explanation

The formula for a solution is as follows:

A*20+(B+C)*11+D*2=100

By modular arithmetic arguments, we see that A and D must differ by a constant amount, such that (A*20+D*2)%11 is constant. In fact D=A+6. The i loop iterates through the three possible values of A.

The value of B can be anything from 1 to 7-i*2 and the total of B and C must be 14-A-D. Thus we obtain the following expressions, which are printed. Ruby allows literal newlines in strings enclosed in ''

   i     |    j
------------------
8-j-2*i  |   i+6

Answer 3

Java, 202 200 198

Trying for the first time :D

EDIT: saved 2 bytes with slightly smaller calculation found in an other comment.

class C{public static void main(String[]c){for(int i=0;++i<5;)for(int j=0;++j<7;)for(int k=0;++k<10;)for(int l=0;++l<10;)if(20*i+11*(j+k)+2*l==100)System.out.printf("%s|%s%n---%n%s|%s%n",i,j,k,l);}}

Answer 4

Batch - 187 bytes

Brute force.

@!! 2>nul||cmd/q/v/c%0&&exit/b
set y=for /l &set z= in (1,1,9)do 
%y%%%a%z%%y%%%b%z%%y%%%c%z%%y%%%d%z%set/aa=%%a%%b+%%c%%d+%%a%%c+%%b%%d&if !a!==100 echo %%a^|%%b&echo ---&echo %%c^|%%d

Un-golfed it's slightly less disgusting:

@echo off
setLocal enableDelayedExpansion
for /l %%a in (1,1,9) do (
    for /l %%b in (1,1,9) do (
        for /l %%c in (1,1,9) do (
            for /l %%d in (1,1,9) do (
                set/aa=%%a%%b+%%c%%d+%%a%%c+%%b%%d
                if !a!==100 (
                    echo %%a^|%%b
                    echo ---
                    echo %%c^|%%d
                )
            )
        )
    )
)

Answer 5

CJam, 40 bytes

A4m*{[KBBY].*:+56=},{:)2/'|f*"
---
"*N}/

The approach for finding the combinations is different from @Optimizer's, but the code for printing them is identical.

Try it online in the CJam interpreter.

How it works

A4m*     e# Push all vectors of length 4 with coordinates in [0 ... 9].
         e# We'd normally use [0 ... 8] here, but "9 4m*" is 1 byte longer and
         e# "A4m*" doesn't produce any false positives.

{        e# Filter the vectors:
[KBBY].* e#   Multiply the elements of the vector by 20, 11, 11 and 2.
:+       e#   Add all four products.
56=      e#   Check if the sum is 56. 56 is used instead of 100 since all elements
         e#   of the vector will be incremented and 56 + 20 + 11 + 11 + 2 == 100.
},       e# Keep only vectors for which = pushed a truthy value.

{        e# For each vector:
:)       e#   Increment each coordinate.
2/       e#   Split into pair.
'|f*     e#   Join each pair, delimiting by '|'.
"
---
"*       e#   Join the two pairs, delimiting by "\n---\n".
N        e#   Push "\n".
}/       e#

Answer 6

Haskell, 125 121 bytes

s=show
f=putStr$unlines[s a++'|':s b++"\n---\n"++s c++'|':s d|[a,b,c,d]<-mapM id$"abcd">>[[1..9]],20*a+11*(b+c)+2*d==100]

Usage:

*Main> f
1|1
---
5|7
1|2
---
4|7
1|3
---
3|7
1|4
---
2|7
1|5
---
1|7
2|1
---
3|8
2|2
---
2|8
2|3
---
1|8
3|1
---
1|9

>> in "abcd">>[[1..9]] makes a list with 4 (length of 1st parameter) copies of the second element, i.e. [[1..9],[1..9],[1..9],[1..9]]. mapM id makes a list of all combinations thereof, i.e [0,0,0,0] to [9,9,9,9]. Keep those that sum up 100 and build a string with the box of it. Print all boxes.

Thanks @Mauris for 1 byte and making me review my post to find 3 more.

Answer 7

Haskell, 107 131 bytes

s=show
r=[1..9]
v=putStr$unlines[s a++"|"++s b++"\n---\n"++s c++"|"++s d++"\n"|a<-r,b<-r,c<-r,d<-r,(2*a+b+c)*10+b+2*d+c==100]

The second version of my first Haskell program ever!

This time with display as per requirements, shamelessly stolen adapted from nimi's (well I did some research but it seems there aren't so may efficient ways to display characters in Haskell so that putStr$unlines is hard to avoid).

And...apart from the factorisation of the formula at the end, it's still readable =)

Answer 8

CJam, 43 42 bytes

A,1>4m*{2/_z+Afb:+100=},{2/'|f*"
---
"*N}/

Explanation to follow.. by today EOD

Try it online here

Answer 9

Python 2, 145 129 Bytes

I'm currently toying with a few different methods of calculating which should be shorter than what is outlined, but I will post what I have now.

i=int
for k in range(1000,9999):
 a,b,c,d=`k`
 if i(a+b)+i(c+d)+i(a+c)+i(b+d)==100and not'0'in`k`:print a+'|'+b+'\n---\n'+c+'|'+d

Answer 10

Python 3, 159

Quick and dirty.

N='123456789'
D='%s|%s\n'
O=D+'---\n'+D
I=int
[print(O%(a,b,c,d)if I(a+b)+I(c+d)+I(a+c)+I(b+d)==100 else'',end='')for a in N for b in N for c in N for d in N]

Answer 11

Java, 450

My first (ungolfed) attempt looked like this:

class B{
  public static void main(String[]a){
    for(int i=1;i<10;i++)
      for(int j=1;j<10;j++)
        for(int k=1;k<10;k++)
          for(int l=1;l<10;l++)
            if(Integer.parseInt(i+""+j)+Integer.parseInt(k+""+l)+Integer.parseInt(i+""+k)+Integer.parseInt(j+""+l)==100){
              System.out.println(i+"|"+j);
              System.out.println("---");
              System.out.println(k+"|"+l+"\n");
            }
  }
}

Answer 12

R, 165 bytes

e=expand.grid(d<-1:9,d,d,d)
a=apply
o=a(e[a(e,1,function(x)20*x[1]+11*(x[2]+x[3])+2*x[4]==100),],1,function(x)cat(x[1],"|",x[2],"\n---\n",x[3],"|",x[4],"\n",sep=""))

This would have been significantly shorter had I chosen to hard-code the output in some way. Like a few other solutions, this takes advantage of the identity 20 x₁ + 11 (x₂ + x₃) + 2 x₄ = 100.

Ungolfed + explanation:

# Create a matrix where each row is a combination of the digits 1-9
e <- expand.grid(1:9, 1:9, 1:9, 1:9)

# Filter the rows of the matrix using the aforementioned identity
e <- e[apply(e, 1, function(x) 20*x[1] + 11*(x[2]+x[3]) + 2*x[4] == 100), ]

# Print each row formatted into boxes
o <- apply(e, 1, function(x) cat(x[1], "|", x[2], "\n---\n", x[3], "|", x[4], sep = ""))

You may be wondering why the last statement is an assignment. As it turns out, the cat function, which concatenates and prints, returns a value of NULL. When you call cat from within a function like apply, the output will be followed by NULL, which is undesirable. There are two ways around this: assign it to a variable or wrap it in invisible. Here I've opted for the former since it's significantly shorter.

You can try it online.

Answer 13

PowerShell , 98

adapted steveverrill's formula

:\>cat printbox.ps1

1..9|%{for($j=1;$j-lt10;$j++){if(($k=(8-$j-2*$_))-gt0){"{0}|{1}`n---`n{2}|{3}"-f$_,$j,$k,
($_+6)}}}

:\>powershell -f printbox.ps1
1|1
---
5|7
1|2
---
4|7
1|3
---
3|7
1|4
---
2|7
1|5
---
1|7
2|1
---
3|8
2|2
---
2|8
2|3
---
1|8
3|1
---
1|9