[Riddler] The Treasure Trove

[Kyle]

You have slayed the monsters, delved deep into the dungeon and you finally find the treasure trove! 100 coins are in the room stacked up in ten stack-
5 stacks of 15 coins, 4 stacks of 5 coins, 1 stack of 4 coins, and 1 stack of 1 coin. Each coin has two identical sides- one made of platinum and one made gold. 20 of the coins are platinum side up and 80 are gold side up. As you go to collect your stash- the evil lich king turns out all the lights and tells you that you can get out alive-- with the gold-- if you can sort the stacks of coins into two groups, each group with an equal number of coins with their platinum faces up.

Rules:

The room is in total darkness and you cannot manifest any light or other means to visually inspect the coins.

Each side of the coins feels identical to its other side.

No use of magic.

You are allowed to flip the coins, but you cannot stand them on edge, or spin them.

How do you sort the coins?

Please provide invisible answers.

[Kyle]

No takers? There's a pretty easy answer to it.

[Mike]

Are coins in any single stack all facing the same way?

[Kyle]

[FlameBlade]

Pretty simple but shocking at first, popular in my circles. Not gonna tell it outright.

[Eliahad]

I feel like it has to have something to do with the fact that there are a lot of odd stacks, but an even number of face up coins. I'm sure the fact that it's a 'pretty simple answer' or 'easy' just means that we'll kick ourselves when we finally hear what the answer is.

[Kyle]

I kicked myself when I finally gave up and heard it. It’s stupid simple.

[FlameBlade]

Solution:

[Mike]

I realized , but that's as far as I got.

I never would have figured this out on my own.

[FlameBlade]

Follow up: what if you had 80 plat coins facing up, instead of 20?

[Kyle]

It’s really such an elegant answer. It’s things like this that make me and my OCD love math.

[Eliahad]