Ways to arrange the integers 1 to 9 with operators so that the result is 100

Question

Prelude:

This task is taken from Five Problems Every Software Engineer Should Be Able to Solve in Less Than an Hour, which I really recommend.

The task:

Write a program that outputs all possibilities to put + or - or nothing between the numbers 1, 2, ..., 9 (in this order) such that the result is always 100.

Winning Criteria:

Shortest code in bytes wins.

Answer 1

Perl 5.10.0 - 50 46 45B

say for grep{eval==100}glob join'{,+,-}',1..9

Usage: perl -M5.10.0 scratch.pl (I think I get the version for free)

Answer 2

CJam, 43 40 bytes

"-"SL]8m*{A,2>.+1\+s}%{~]:+100=},N*S/'+*

Here is how it works:

"-"SL]                     e# This is an array containing -, space and empty character
                           e# This represents -, + and joints correspondingly
      8m*                  e# Get all cartesian products of these 3 strings of length 8
                           e# For instance, all cartesian products of length 2 are:
                           e# [["-" " "] ["-" "-"] ["-" ""] [" " " "] [" " "-"] [" " ""]
                           e# ["" " "] ["" "-"] ["" ""]]
         {          }%     e# Map these cartesian products over this loop
          A,2>             e# Get array [2, 3, 4, 5, 6, 7, 8, 9]
              .+           e# In-order concatenation of the above two arrays
                1\+s       e# Prepend 1 to the result from above and convert it to string
{        },                e# Now we have all possible strings of 1 to 9 with all possible
                           e# operators as well as joins (things like 567). Its time to
                           e# filter out what add up to 100
 ~                         e# Evaluate the string. This leaves some numbers on stack.
  ]:+                      e# Wrap those numbers in an array and take their sum
     100=                  e# Check if the sum is equal to 100
           N*              e# Join all filtered strings by newline
             S/'+*         e# We used space instead of +. So now we replace space with +

Try it online here

Answer 3

My shot at this:

Python 2, 93 bytes

def a(e,i):
 if i<=9:[a(e+x+`i`,i+1)for x in("+","-","")]
 elif eval(e)==100:print e
a("1",2)

Answer 4

Mathematica, 93 92 bytes

Print/@Select[""<>ToString/@Range@9~Riffle~#&/@{"+","-",""}~Tuples~{8},ToExpression@#==100&]

Fairly straightforward: generates all possible strings using Tuples and then filters them.

For reference, I get:

1+2+3-4+5+6+78+9
1+2+34-5+67-8+9
1+23-4+5+6+78-9
1+23-4+56+7+8+9
12+3+4+5-6-7+89
12+3-4+5+67+8+9
12-3-4+5-6+7+89
123+4-5+67-89
123+45-67+8-9
123-4-5-6-7+8-9
123-45-67+89

Answer 5

Pyth, 26 bytes

fqvT100m+ssC,r1Td9^c3"+-"8

First, we generate all 8 element combinations of ["+", "-", ""]. c3"+-" chops "+-" into 3 rougly equal sied pieces, giving the appropriate list. ^c3"+-"8 gives the 8 element combinations.

Then, we greate the arithmetic sequences. C,r1Td zips together the operators with the numbers 1 through 8, which are then summed twice to give the string, and + ... 9 puts a 9 at the end.

Finally, fqvT100 filters for those expressions which evaluate to 100.

---

The update to the interpreter which allowed this code to work was this one, which was made about a day before this question was asked, so this code would have only worked on the command line compiler, not the online one, when the question was asked.

Demonstration.

Answer 6

JavaScript, 86 92

Head to head with the best. That must be an anomalous problem.

Edit -6 thx @nderscore

for(i=6562;k=--i;eval(o)-100||alert(o))for(j=o=1;j++<9;k=k/3|0)o+=k%3?' +-'[k%3]+j:[j]

Test in any browser console, it pops up just 11 times.

Or this snippet:

function out(x) { OUT.innerHTML = OUT.innerHTML + '\n' + x; }

// 6562 is 3 powered to 8 +1
for(i=6562;k=--i;eval(o)-100||out(o))
  for(j=o=1;j++<9;k=k/3|0)
    o+=k%3?' +-'[k%3]+j:[j]
    

<pre id=OUT></pre>

Answer 7

Python (176)

39 minutes and counting (for all problems that is)

from itertools import*
for i in product(('+','-',''),repeat=8):
 s=''.join(''.join(j)for j in chain(izip_longest(map(str,range(1,10)),i,fillvalue='')))
 if eval(s)==100:print s

This could probably be shorter, but this was my actual solution for this problem, just golfed down a bit.

Answer 8

K, 61 50 bytes

t@&100=.:'t:{:[x>9;,y;,/_f[x+1]'(y,"+";y,"-";y),\:$x]}[2;"1"]

Tested with Kona.

The general approach is to recursively generate all the expressions and then filter out those which eval (.) to 100. This is reasonably competitive as written, but I think there's still room for improvement.

edit:

t@&100=.:'t:(,"1"){,/x,/:\:("+";"-";""),\:$y}/2+!8

Altering my approach a bit to be iterative rather than recursive, which removes the need for explicit base cases as well as saving me some brackets.