The Great Candy Hunt

There's treasure everywhere...

On Easter morning, my parents would put candy in brightly-colored plastic eggs and hide the eggs around the house. “Hide” might be a little strong, actually. The eggs were only in one room of the house, and almost all of them were in plain sight – between couch cushions, on top of books, next to records. My three siblings and I had to close our eyes while the eggs were hidden, and then when my parents said “Go!” we’d scramble to stuff as many as we could into our Easter baskets.

Once I found an egg, it was generally pretty easy to grab it. Opening the eggs was easy too.

And in this way, math test prep is very much like my family’s Easter egg hunts. There are lots of easy points – questions that a student doesn’t currently know but could master very easily. Maybe it’s that exponent rule you forgot (“Bases same, add”). Maybe it’s that one missing step in a process (“How do I find the radius in a circle equation after completing the square?”). Or maybe it’s that simple concept you never learned (“What’s margin of error?”). They aren’t that hard – you just have to find them.

The Great Question Hunt

Good news: you don’t have to worry about your older brother hipchecking you into the wall for this particular hunt. You’re all alone in the room, so you can go after any eggs you want, and you’ll be free to open all of your eggs without interference at the end of the hunt.

But each egg has some sort of unlocking mechanism – a latch to open, a knot to untie. Some can be opened in a few seconds, while others might take as long as a minute to open. However, once you know the mechanism really well, you can manipulate it almost without thinking, kind of like tying your shoe or taking off your jacket.

Many of these mechanisms repeat themselves entirely from one egg to the next, or share certain steps (unlatch this, twist that). And most kids have seen all of these mechanisms before in previous hunts.

There is one complication: there are thousands of eggs in the room…and some of them have already been plundered. But all of the eggs were re-closed after the candy was removed, so there’s no way to tell which ones have candy just by looking at them.

You, an experienced egg hunter of many years, know every single egg in the room. You can open every mechanism. You even know which sizes, shapes, colors, and mechanisms tend to go together. And you can use this knowledge to predict which eggs a kid could open, based on what’s in his basket.

You’ve been asked to help your plucky young nephew collect as many eggs as possible. You can’t actually pick the eggs or open them, but you can give him advice. He shows up with zero eggs in his basket. And though knows how to open some of the eggs, he doesn’t seem to remember which ones.

So you have a search problem. You know every egg in the room and could open any of them yourself, but you don’t know which ones your nephew has already opened or is capable of opening. He has some knowledge of where the eggs are and which ones he has opened, but it’s limited. You have to work together to find the eggs he can open that still have candy in them as fast as possible.

And there's actually one other little problem: if a kid hasn't opened a particular lock or untied a specific knot for a while, he'll forget, and then he'll have to learn how to open it again.

How long is too long? It's tough to say. Certainly opening the same egg every day for a month is overkill. If your nephew is careful about which ones he practices, he could actually maintain a lot of eggs at once by strategically practicing the mechanisms they have in common. But if an egg has a really complex mechanism, with steps that aren’t required by any other egg, and he doesn’t practice that mechanism for a whole month, he probably won’t be able to open it.

One interesting thing about this situation: your nephew can do a lot of the work himself. If he strolls around the room, checks every egg, puts the candy-filled ones in his basket, and periodically retries the tough-looking mechanisms in his basket, he’ll get a lot of candy.

But he gets frustrated easily, especially when the eggs won’t open right away. Oddly, he doesn’t mind opening the eggs he’s already figured out, even when they don’t have any candy in them. But he hates to retry the ones he couldn’t open previously, even when he can hear the rattle of jelly beans inside.

Of course, you could just accompany him on the entire hunt: point out which eggs to try, help him work through the mechanisms, educate him on the similarities between the different locks and latches and knots, encourage him to periodically retry the ones in his basket. But that would take a lot of your time – there are thousands of eggs, and this hunt may not be over for a few months.

How can you help?

1. You want your nephew to find and open a lot of eggs, then bring you the results.

2. You want to improve the quality of his search over time: “Look for more of these red ones and these ones with this type of knot. Don't waste time on yellows.”

3. You want him to also periodically reopen the tough eggs in the basket.

Some interesting points here:

• It’s not uncommon for you to reject an egg, or a whole swath of eggs, if you don’t think they will yield anything. In fact, quickly assessing the value of a particular egg for a particular kid and allocating time accordingly is a major part of your job.

• Once you've seen enough eggs in his basket and have narrowed the scope of his search, you don't actually care which ones your nephew works on. You'll never know for sure how many jellybeans are in a particular egg - you just want him gathering and trying ones with a high expected value.

• You do spend some time teaching him the mechanisms, but not as much as an outsider might think. It would be foolish to spend thirty minutes on one tricky lock, for example. Think of how many times he’ll have to redo that one to keep it fresh. And what if there aren't any other locks like it? He'd be much better off spending those thirty minutes relearning 5 common mechanisms and quizzing himself on 10 eggs he recently acquired.

• An extremely high percentage of the real work is done by your nephew. He's the one going through all the eggs, trying to open them, and bringing you the results. Even when you’re with him, the kid is the one trying to open the eggs. So you need to motivate him. If he has any energy for the search - the excitement of opening an egg and catching the jelly beans as they flow out, perhaps, or the anticipation of opening piles of eggs - you have to understand that energy and connect it to your plan. He has to know exactly how all the work you’re proposing will get him what he wants.

My parents got to watch the full hunt, from the wild scramble at the beginning to the unseemly jellybean chugs at the end. My students eat their jellybeans alone. But I think I enjoy hearing about it just as much as my parents enjoyed watching.

And I don’t have to worry about them eating too much.