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// SPDX-License-Identifier: MIT
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pragma solidity ^0.8.17;
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import "./IPuzzle.sol";
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// Hello, it's me your Doordash shopper. I'm at the grocery store.
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// I'm having trouble finding the ingredients you requested for your fruit punch.
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// Can you help me find them?
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// There's only 906459278810089239264754550292645448950 places to check...shouldn't be so bad.
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//
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// Enjoy this kind of challenge? Consider working at Zellic: [email protected]
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//
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contract Chal is IPuzzle {
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    uint256 constant punch = 906_459_278_810_089_239_293_436_146_013_992_401_709;
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    function name() external pure returns (string memory) {
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        return "Groovy Fruit (Punch) Fiesta";
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    }
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    function generate(address _seed) external pure returns (uint256) {
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        uint256 fiesta = uint256(keccak256(abi.encodePacked(_seed))) % punch;
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        fiesta = (fiesta % 10_000_000_000_000_000_000_000) + 10_000_000_000_000_000_000_000;
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        return fiesta;
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    }
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    function verify(uint256 _start, uint256 _solution) external pure returns (bool) {
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        uint256 apple = _solution & 0x7fffffffffffffffffffffffffffffff;
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        uint256 banana = (_solution >> 128) & 0x7fffffffffffffffffffffffffffffff;
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        uint256 cherry = 1;
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        if (apple < 100 || banana < 100) {
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            return false;
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        }
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        if (smoothie(apple, banana) != 1) {
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            return false;
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        }
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        return _start
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            == (
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                (apple * milkshake(banana + cherry)) % punch
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                    + (banana * milkshake(apple + cherry)) % punch
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                    + (cherry * milkshake(apple + banana)) % punch
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            ) % punch;
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    }
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    function milkshake(uint256 apple) private pure returns (uint256) {
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        int256 appleJuice_;
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        (, appleJuice_,) = blender(apple, punch);
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        require(appleJuice_ > 0);
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        uint256 appleJuice = uint256(appleJuice_);
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        require((apple * appleJuice) % punch == 1);
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        return (appleJuice % punch + punch) % punch;
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    }
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    function blender(uint256 apple, uint256 banana)
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        private
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        pure
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        returns (uint256 yummy, int256 appleJuice, int256 bananaJuice)
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    {
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        if (banana == 0) {
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            return (apple, 1, 0);
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        }
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        (uint256 _yummy, int256 _appleJuice, int256 _bananaJuice) = blender(
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            banana,
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            apple % banana
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        );
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        (yummy, appleJuice, bananaJuice) =
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            (_yummy, _bananaJuice, _appleJuice - int256(apple / banana) * _bananaJuice);
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    }
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    function smoothie(uint256 apple, uint256 banana) private pure returns (uint256 yummy) {
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        (yummy,,) = blender(apple, banana);
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    }
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}
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