Life is A Test 2: Test Harder (Quite A Bit Harder)

by Brony_of_Brody

Welp. Hard To Argue Against That

The whole spam-letter thing was indeed a clever prank. Rather unfortunately, the follow-up response on Black Bird's part proves to be somewhat irrefutable - she knocks you out with sleeping gas, marenaps the pair of you, and now you and Rainbow Dash have found yourselves locked in a small dungeon somewhere, with what appears to be a small, but very long table in front of the pair of you. The accommodations seem pretty roomy, but someone ought to plug that infernal leak. And there's too many spiders. Gingerbread spiders. Well, at least you won't starve. You hope.

This is why barbarians are so hard to argue with - there's no clever answer to death. Or worse.

After determining to your dissatisfaction that there are no windows and the only securely barred door cannot be opened, you spot a note right on the table's left end.

Greetings, you blue troglodyte and you ordinary looking royal flank-kisser, it reads. I have arranged for you to play a little game of mine, and I'm pretty confident that Rainbow Crash isn't lucky or smart enough to win, prepare to be stuck forever while you struggle for my amusement.

Here are the rules: on the table right in front of you are a hundred coins, in Equestrian bits. The values of each coin is different from the others - some are worth one bit, others two, and so on. The pair of you will take turns, picking off coins from each end (you can freely choose which end every turn, of course), until the last one is gone. Whoever has the most bits at the end of the game wins.

But I'm not that nice. The pair of you only get to go free if Rainbow wins the game, and I am trusting you to play at your best, Mister Royal Dispute Settler On Probation, because I'm watching, and if I suspect you went easy on her, you can enjoy rotting here forever. With the hungry GIANT gingerbread spiders in the cell next door.

And don't worry. Should Rainbow lose, the coins will randomise themselves and give you another chance, but as if Rainbow ever will win. I'll even let her go first for the first attempt.

Have fun. And don't tell her the solution, mister. I'm always watching and listening.

Yours insincerely,

Black Bird

You look up. Sure enough, there appears to be a two-way crystal ball, observing your every move. Well, horse-manure. Rainbow has to figure this puzzle out herself, and to make matters worse, you're obliged to make it as difficult for her as possible. But all the same, you and Rainbow have solved puzzles together in the past. No choice but to trust Rainbow is smarter than she appears to be and learned a few tricks. So how can Rainbow win the game and free the pair of you, so that you can continue to plot revenge in this prank-war gone too far?

Author's Note:

Oh dear. Act as the voice in Rainbow's head and get her out this jam. Please.

1. One hundred coins laid out in a row on a table.
2. The coins are of different values.
3. You and Rainbow Dash take turns pocketing one coin at a time. Only coins at the end of the row can be picked.
4. Both you and Rainbow Dash can choose which end to pick from every turn.
5. Whoever gathers the most money when the last coin is gone wins. You will only go free if Rainbow Dash gets more money than you and wins.
6. Rainbow Dash goes first.

PUZZLE: How can Rainbow Dash make more money than you and go free?

Comments

[Duckgame4life]

Well this is tough
minimum score is 50-51 as at least 1 coin is different value then the others but unless you can tell them apart then i have no clue how to rig it

[SisselSandvich]

I think we can assume that we can tell how many coins each bit is worth. Otherwise it would be pure luck.

Having said that, let's color the coins alternating colors, red and blue. Now, consider what happens when Rainbow Dash and I each pick a coin. Since there are an even number of coins, the coins on the ends have to be opposite colors - one red, one blue. But after Rainbow Dash picks her coin, the coins left are the same color - either both red or both blue, opposite the color of the coin Rainbow Dash picked. This means that whenever Rainbow Dash picks a red coin, I have to pick a blue coin, and vice-versa. Rainbow Dash always has free choice of what color coin she wants, while I have to choose the opposite color of her (though I get to choose which one I take at any given moment except the last coin). This means that Rainbow Dash could choose to, for example, always take the red coin, and I would be forced to always take a blue coin. That would give Rainbow Dash all the red coins, and me all the blue coins. Of course, she could also take all of the blue coins and force me to take all of the red ones. So to win, Rainbow Dash can just sum up all of the red coins, then sum up all of the blue coins, and take whichever color is worth more in total.

Granted, this plan assumes that the red coins and blue coins do not sum to the same value. There are potential countermeasures Rainbow Dash can take in this case, such as taking the lead and then switching colors, but I can come up with arrangements where this is impossible. For example, if the coins increase from each end so that the end coins are both 1, second from the end are both 2, and so on up to two 50 coins in the center, then I can force a tie by always taking the largest coin available (in the first 25 rounds I'll always take at least one more bit per round than Rainbow Dash will, and in the last 25 rounds she'll only be able to take at most one more bit per round than I will). Since ties are never mentioned, I'm going to assume that all 100 coins together sum to an odd total, so that a tie is impossible.

[ANW]

This prank war has just became dangerous.
It's time to stop.
And question why everything seems to be a puzzle.
I mean, just getting breakfast was a puzzle itself.