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! Can you escape from Dr. Schrödinger’s lair and save the day? Dan Finkel shows how.

**Transcript:**

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?

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.