solve: http://www.matrix67.com/blog/archives/4790

test768b.js

var input = 2011,
output = 2012,
depthLimit = 30,
countLimit = 100000;
count = 0,
depth = 0,
comp = [
    function(x){return x+7},
    function(x){return x/2},
    function(x){return x*3},
    function(x){return x-5;}
],
symbol = [
    '+7 ',
    '/2 ',
    '*3 ',
    '-5 '
],
path = [
    [1,2,3],
    [0,2,3],
    [0,1,3],
    [0,1,2]
],
results = [],
run=function (which,route,val) {
    if(count>countLimit || depth>depthLimit || Math.round(val)!==val) {
        return;
    }
    count++;
    console.log(count + ':' + depth + ':' + val);
    if(val===output) {
        var next = [];
        for(var i=0;i<route.length;i++)
            next[i]=route[i];
        next.push(which);
        results.push(next);
    }
    route.push(which);
    for(var i=0;i<path[which].length;i++) {
        depth++;
        if(path[which][i] !== which)
            run(path[which][i], route, comp[which](val));
        depth--;
    }
    route.pop();
}
run(0,[],input);
results.forEach(function(v) {
    var str = input+' ';
    v.forEach(function(i) {
        str += symbol[i];
    });
    str += '= ' +output;
    console.log(str);
});