The villainous Dr. Schrödinger
has developed a growth ray and intends to create
an army of giant cats to terrorize the city. Your team of secret agents has tracked him
to his underground lab. You burst in to find… that it’s a trap! Dr. Schrödinger has slipped
into the next room to activate his device and disabled the control
panel on the way out. Fortunately, your teammates are
masters of spy-craft. Agent Delta has hacked
into the control panel and managed to reactivate
some of its functionality. Meanwhile, Agent Epsilon has
searched through surveillance to find the code for the door: 2, 10, 14. All you have to do is enter those numbers
and you’ll be free. But there’s a problem. The control panel has only three buttons: one which adds 5 to the display number, one which adds 7, and one which takes the square root. You need to make the display output
the numbers 2, 10, and 14,
in that order. It’s okay if it outputs different
numbers in between, but there’s no way to reset the display, so once you get to 2, you’ll have to continue
on to 10 and 14 from there. Not only that, Agent Delta explains that there are other traps
built into the panel. If it ever shows the same number
more than once, a number greater than 60, or a non-whole number, the room will explode. Right now, the display reads zero,
and time is running out. There’s only one way to solve the puzzle,
with a few small variations. How will you input the code to escape
from Dr. Schrödinger’s lair and save the day? Pause the video now if you want
to figure it out for yourself! Answer in: 3 2 1. You look over your options. Adding 5 or 7 increases the number, and the square root button
will make it smaller. But there are only a few options
where you can use that button: 4 9 16 25, 36, and 49. You’d love to make 4 or 16. Then you could hit the square root button
once or twice to get 2. But you can’t make either with
just the 5 and 7 buttons. What will you do? You look at the other possible options for
numbers you could take the square root of. Nine you can’t reach. Twenty-five and 49 would take you back to
5 or 7, and you can already get to each
of those. Thirty-six is your only option. You add 5, 7, 5, 7, 5, 7, and then hit the square root button. Why that series of 5s and 7s? It’s somewhat arbitrary, but you know that you want
to avoid 10, 14, and perfect squares, since you’ll need them later. This gets you to 6. Does that help? Looking at your options,
you see that 16 is now in your sights. You add 5 twice more to reach it. Then hit square root twice. That gets you to 2. You’re on your way! Now to 10. You can’t get straight
there through addition alone, so you’re going to have
to reach another square. Taking the square root of 9 or 25 would
get you to a good place, but it turns out that 25
is unreachable from 2. So you add 7 to get to 9, then take the square root again. That gets you to 3. Adding 7 again makes 10. Finally, you need to reach 14. Thinking backwards, you imagine where
you could be before 14: 7 or 9. But 9 won’t work because
you’ve already used 9. However, you could get to 7
by reaching 49 first. You add your way towards it, being careful not to hit any
of the numbers you’ve hit so far. You thread your way carefully, adding five 5s and two 7s. Then, square root to 7, and add 7 more. The door opens,
and you’re out of the trap. Thanks to your problem-solving skills, your team gets Schrödinger’s cats out
of the box in the nick of time. As for Schrödinger,
you can be certain of one thing: he’ll be spending quite some
time in a box of his own.
