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In which Restaurant can I get the most profit from in comparison to the others?

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Le Nah?
Le Yeah?
Le Wow?
Or the Sushi High Roller?

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Le wow is better

First, you need 2 high level Pokemon (70 or higher), preferably ones who can use moves like earthquake or surf ( I use Charizard and Flygon). Make sure they also have a stalling move (Like fly or a move like sword dance) so you can complete the exact turns you need to complete.

After you need an amulet coin (to increase money earning) and prize money O-Power (level 3 preferably) or a friend who can use it.

Now, have your two high levels in slot 1 and 2 of your party. Make sure one has the amulet coin. Walk into Le Wow and use the Prize Money O-Power. Then talk to the lady. Choose the double battle and pay her 100K (Can be lowered, not sure how). Now, you go through a series double battles. Each double battle gives prize money ( and good EXP for leveling Pokemon). Try to win the battles in the target time stated for more end money. Once all of the battles are over, you are rewarded Balm Mushrooms, which go for 6K each. If you get all of the battles in the correct amount of turns ( and none of your Pokemon fainting), you get 25 Balm Mushrooms. (150 000k $ without the amulet coin)

25 * 6000 = 150000 Poke, which is more than you had to pay to enter. Also, you get 10K for the first 2 battles (Without Amulet Coin) and 4K for the last 3 battles (Without Amulet Coin).

150000 + (20000 2) + (8000 3) = 24000 + 40000 + 150000 = 214000 Poke per run. That did not include the Prize Money O-Power, but it did include the Amulet Coin.

214000 - 100000 (Fee to enter) = 114000 Poke profited per run, if everything goes right.

With the new Event Inkay (with a move called Happy Hour) you can make EVEN more money. But, as of now, it is a Japanese only event. The move increases the money earned from battles.

If you throw in PayDay, you can get EVEN more money. PayDay takes the level of the user, multiplies it by 5 (in gen 3 or higher) and scatters coins of those value. AND, it is effected by Amulet Coin (Pokebank will allow you to move a Meowth/Persian up to X and Y). And then at the end of the battle, you pick the money and it is added to your amount.

If you complete the Le Wow challenge perfectly at least once, the cost for it lowers.

If you use Amulet Coin + Prize Money O-Power 3, and have the discount, you earn a total of 150000 + (60000 2) + (24000 3) - 90000 = 252000 per run, plus lots of EXP.

Hope I helped! :D

Source: experience and with the help of a calculator

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You can always go to the elite 4 if you dont have enough money
Ahh! to much maths! ut thanks anyways
Lol but you need math to know witch one makes the most money