assignment: https://www.youtube.com/watch?v=HyRjuPP9S3o

secret-sauce-riddle-puzzle.js

var optSafeId = Array.from({ length: 1300 - 13 + 1 }, (_, i) => i + 13)
var perfectCube = i => Math.round(i**(1/3))**3 === i // float fuckup
var perfectSquare = i => Math.round(i**(1/2))**2 === i // float fuckup
var lg500 = i => i > 500 
var secDig1 = i => i.toString().substr(1, 1) == '1'
var truth = (isTruth, val) => isTruth ? val : !val

// combinatorics hacked by bin numbers
var possibleResponses = Array.from({ length: 2 ** 4 })
    .map((_, i) => i.toString(2).padStart(4, '0')) 
    .map(([q1, q2, q3, q4]) => [q1 === '1', q2 === '1', q3 === '1', q4 === '1'])

var getOptSafeIdFor3Rules = ([q1, q2, q3]) => optSafeId
        .filter(i => truth(q1, lg500(i)))
        .filter(i => truth(q2, perfectSquare(i)))
        .filter(i => truth(q3, perfectCube(i)))

var getOptSafeIdFor4Rules = ([q1, q2, q3, q4]) => getOptSafeIdFor3Rules([q1, q2, q3]).filter(i => truth(q4, secDig1(i)))
    
var lupici = possibleResponses
    .map((rules) => ({ rules, optionsAfterThirdQ: getOptSafeIdFor3Rules(rules) }))
    .filter((i) => i.optionsAfterThirdQ.length === 2) // check that only 2 options left before fourth question was asked
    .map(i => ({ ...i, finalOptions: getOptSafeIdFor4Rules(i.rules) }))
    .filter((i) => i.finalOptions.length === 1)

var benga = lupici
    .flatMap(i => [
        // check all options if fourth question is true | false
        [[!i.rules[0], !i.rules[1], i.rules[2], true], i],
        [[!i.rules[0], !i.rules[1], i.rules[2], false], i]
    ])
    .map(([rules, lupic]) => ({
      rules,
      lupic,
      finalOptions: getOptSafeIdFor4Rules(rules),
    }))
    .filter(({ finalOptions }) => finalOptions.length === 1)

console.log('benga found options: \n', benga.map(i => i.finalOptions.join(',')).join('\n'))

xd.js

var perfectCube = n => Math.floor(n**(1/3)) === n**(1/3)


/*
>>> np.cbrt([64])
array([4.])
>>> 64 ** (1/3)
3.9999999999999996
>>> import numpy as np
>>> np.cbrt(64)
4.0
*/

/*
64 ** (1/3) === Math.cbrt(64)
*/