Various logic/programming challenges I've seen in interviews...

skittles.js

var assert = {
    test: 1,
    equal: function(exp, target) {
        console.log("[test](%d) expected "+target+" got " + exp + " (%s)", this.test++, (exp == target ? 'SUCCESS' : 'FAIL'));
    }
};

// SKITTLES
// Given a target goal in kilograms, and a number of
// small bags of skittles (1kg) and large bags of skittles (5kg)
// return the number of small bags used to make up the total,
// assuming we'll use as many big bags as possible.
// If not possible, return -1.
//
function createPackage(small, big, goal) {
    var lg = Math.floor(goal / 5),
        sm = Math.floor(goal - lg);
    
    goal = goal - ((big <= lg) ? (big*5) : (lg*5));
    return (small >= goal) ? goal : -1;
}

assert.equal(
 createPackage(4, 1, 9),
 4
);

assert.equal(
 createPackage(4, 1, 10),
 -1
);

assert.equal(
 createPackage(4, 1, 7),
 2
);

assert.equal(
 createPackage(6, 2, 7),
 2
);

assert.equal(
 createPackage(4, 1, 5),
 0
);

assert.equal(
 createPackage(4, 1, 4),
 4
);

assert.equal(
 createPackage(5, 4, 9),
 4
);

assert.equal(
 createPackage(9, 3, 18),
 3
);

console.log('Success!');

triplethreat.js

var assert = {
    test: 1,
    equal: function(exp, target) {
        console.log("[test](%d) expected "+target+" got " + exp + " (%s)", this.test++, (exp == target ? 'SUCCESS' : 'FAIL'));
    }
};

// TRIPLE THREAT
// Determine if an array has 3 consecutive
// increasing, adjacent numbers anywhere.
// Return true or false.
//
function tripleThreat(list) {
    var found = false,
        len = list.length;
    for (var i=0; i < len; i++) {
        if (i <= (len - 3) && list[i]+1 == list[i+1] && list[i]+2 == list[i+2]) {
            found = true;
            break;
        }
    }
    return found;
}

assert.equal(
  tripleThreat([1, 4, 5, 6, 2]),
  true
);

assert.equal(
  tripleThreat([1, 2, 3]),
  true
);

assert.equal(
  tripleThreat([1, 2, 4, 5, 7, 6, 5, 6, 7, 6]),
  true
);

assert.equal(
  tripleThreat([1, 2, 4, 5, 7, 6, 5, 7, 7, 6]),
  false
);

assert.equal(
  tripleThreat([1,2]),
  false
);

assert.equal(
  tripleThreat([10, 9, 8, -100, -99, -98, 100]),
  true
);

assert.equal(
  tripleThreat([10, 9, 8, -100, -99, 99, 100]),
  false
);

I was given these in an email questionnaire and told to basically "fill in the function to complete the below tests successfully" and to have it done and posted as a Gist for review in 20min. I only got one of them in 20 minutes; but these are the completed functions, after having spent a bit more time thinking about it during and after dinner the same evening.

These types of questions are horrible to ask interviewers in general; much less given the time frame and context in which they were administered here. These types of questions only test to see if the interviewee has ever had these same questions before - they do not test your knowledge, ability, creative and commitment as a front-end developer at all.