cat_army.js

// Original TED Riddle Video: https://www.youtube.com/watch?v=YeMVoJKn1Tg

// check if number valid
function state_is_valid(array, two_found, ten_found){
    // whole number
    // not great than 60
    // no duplicates
    const last_num = array[array.length-1];
    const normal_check =  Math.floor(last_num) == last_num && last_num <= 60 && !has_duplicates(array);
    if(normal_check){
        if(two_found){
            // array needs to have a 2
            if(array.indexOf(2) < 0){
                return false;
            }
            if(ten_found){
                // array needs to have a 10
                if(array.indexOf(10) < 0){
                    return false;
                }
            }
        }
        return true;
    }
    return false;
}

function has_duplicates(array){
    const history = {};
    for(const num of array){
        if(!history[num]){
            history[num] = 1
        }else{
            return true;
        }
    }
    return false;
}

// returns true if array has solution
function is_solution(array){
    // has numbers 2, 10, and 14 in order
    const solutions = [2, 10, 14]

    for(const num of array){
        if(num == solutions[0]){
            solutions.shift();
            if(!solutions.length){
                return true;
            }
        }
    }
    return false;
}

// main
function main(){
    // keep running queue of objects
    const queue = [[0]];
    let [two_found, ten_found] = [false, false];
    while(queue.length){
        const curr_state = queue.shift();
        const curr_num = curr_state[curr_state.length - 1];
        // try all 3 possibilities
        // +5, +7, sqrt
        const possibilities = [curr_num + 5, curr_num + 7, curr_num ** .5];
        for(const possibility of possibilities){
            new_state = [...curr_state];
            new_state.push(possibility);
            if(!two_found && possibility == 2){
                two_found = true;
            }else if(two_found && !ten_found && possibility == 10){
                ten_found = true;
            }
            if(state_is_valid(new_state, two_found, ten_found)){
                if(is_solution(new_state)){
                    // stop when solution found
                    return console.log("SOLUTION! ", new_state.join(", "));
                }
                queue.push(new_state);
            }
        }
    
    }
}

main();