kepo-ing Zz85

At the Stanford Alumni Job Fair today, Shop It To Me has an unique way of recruiting/attracting developers.

So here, interested developers were challenged to solve a puzzle written on the black board.

Being a fan of puzzles (and a fan of the bulb puzzle), I gave it a try.

Here’s how the puzzle goes

Assuming 100 switches for 100 lights are switched off. First, toggle every switch the 1st round. The 2nd round, toggle every 2nd switch (from the start) of 100. 3rd round, toggle every 3rd switch. This goes on until the 100th round. Which lights are turned on and why?

Being unwilling to do too much thinking mentally, I wipe out my laptop to write a simple javascript script to solve this quickly.

<!– solve_puzzle.html –>
<!– easy way of solving the 100 switches puzzle by joshua koo –>
<textarea id="console" style="width:400px; height:300px">
This is a simple way to display output
</textarea>
<script>
// Let 100 lights/switches be an array
var lights= new Array();

// All switches are turned off. Not neccessary but may initialize them as false
//for (var i=1;i<=100;i++) { lights[i] = false; }

for (var i=1;i<=100;i++) { // For 100 rounds
for (var j=i;j<=100;j+=i) { // Start with the number and incriment itself
lights[j] = !lights[j]; // Toggle the switch
}
}

// Display the result
for (var i=1;i<=100;i++) {
if (lights[i]) document.getElementById(’x').value += i + "\n";
}
</script>

So this is a programmatic solution to the puzzle. For a more mathematical + logical solution read this.