Super-hacky solver for the "Gopher Holes" puzzle: http://amzn.to/2hqLO2V

block-puzzle.js

/**
 * Super-hacky solver for the "Gopher Holes" puzzle:
 * http://amzn.to/2hqLO2V
 *
 * Note: I assumed that the blocks would be going vertically in one direction
 * and horizontally in another.
 *
 * Also: I wrote this for fun over the holidays - I'm sure this code is
 * terrible and could be improved. It was good enough for my needs!
 *
 * By John Resig <jeresig@gmail.com>
 * License: Public Domain
 */

const blocks = [
    // Duplicates
    {
        top: [-1, 1, 0],
        bottom: [-1, 0, 1],
    },
    {
        top: [-1, 1, 0],
        bottom: [-1, 0, 1],
    },

    // Others
    {
        top: [1, -1, 0],
        bottom: [0, -1, 1],
    },
    {
        top: [1, 0, 0],
        bottom: [0, 1, 1],
    },
    {
        top: [1, -1, -1],
        bottom: [0, -1, -1],
    },
    {
        top: [1, 0, 1],
        bottom: [0, 1, 0],
    },
];

const numBlocks = blocks.length;
const numOptions = 4;
const options = [];
const initialArray = [];
const allOptions = [];
const optionNames = ["top", "bottom", "top reversed", "bottom reversed"];
let count = 1;

for (const block of blocks) {
    options.push([
        block.top,
        block.bottom,
        block.top.slice(0).reverse(),
        block.bottom.slice(0).reverse(),
    ]);
}

// From: https://stackoverflow.com/questions/9960908/permutations-in-javascript/37580979#37580979
function* permute(permutation) {
    const length = permutation.length;
    const c = Array(length).fill(0);
    let i = 1;

    yield permutation;

    while (i < length) {
        if (c[i] < i) {
            const k = (i % 2) ? c[i] : 0;
            const p = permutation[i];
            permutation[i] = permutation[k];
            permutation[k] = p;
            ++c[i];
            i = 1;
            yield permutation;
        } else {
            c[i] = 0;
            ++i;
        }
    }
}

function* genOptions() {
    const max = Math.pow(numOptions, numBlocks);
    for (let i = 0; i < max; i++) {
        yield ("000000" + (i).toString(4)).slice(-6).split("");
    }
}

function check(posA, posB) {
    return (posA !== 1 && posB !== 1 || posA === -1 && posB === 1 ||
            posA === 1 && posB === -1);
}

for (let num = 0; num < numBlocks; num++) {
    initialArray.push(num);
}

for (const option of genOptions()) {
    allOptions.push(option);
}

// Go through all of the possible block options
for (const permutation of permute(initialArray)) {
    for (const option of allOptions) {
        count += 1;

        const bottom = [
            options[permutation[0]][option[0]],
            options[permutation[1]][option[1]],
            options[permutation[2]][option[2]],
        ];
        const top = [
            options[permutation[3]][option[3]],
            options[permutation[4]][option[4]],
            options[permutation[5]][option[5]],
        ];

        if (check(bottom[0][0], top[0][0]) &&
            check(bottom[1][0], top[0][1]) &&
            check(bottom[2][0], top[0][2]) &&
            check(bottom[0][1], top[1][0]) &&
            check(bottom[1][1], top[1][1]) &&
            check(bottom[2][1], top[1][2]) &&
            check(bottom[0][2], top[2][0]) &&
            check(bottom[1][2], top[2][1]) &&
            check(bottom[2][2], top[2][2])) {
                console.log("MATCH");
                console.log("BOTTOM:",
                    permutation[0], optionNames[option[0]],
                    permutation[1], optionNames[option[1]],
                    permutation[2], optionNames[option[2]]);
                console.log(bottom[0][0], bottom[1][0], bottom[2][0]);
                console.log(bottom[0][1], bottom[1][1], bottom[2][1]);
                console.log(bottom[0][2], bottom[1][2], bottom[2][2]);
                console.log("TOP:",
                    permutation[3], optionNames[option[3]],
                    permutation[4], optionNames[option[4]],
                    permutation[5], optionNames[option[5]]);
                console.log(top[0][0], top[0][1], top[0][2]);
                console.log(top[1][0], top[1][1], top[1][2]);
                console.log(top[2][0], top[2][1], top[2][2]);
        }
    }
}

console.log("Checked:", count);

gistfile1.txt

$ time node block-puzzle.js
...
MATCH
BOTTOM: 3 top reversed 2 bottom reversed 1 bottom reversed
0 1 1
0 -1 0
1 0 -1
TOP: 4 bottom 5 bottom reversed 0 bottom
0 -1 -1
0 1 0
-1 0 1
Checked: 2949121

real	0m0.547s
user	0m0.515s
sys	0m0.034s