Mysty: Rhem 2
Buy Rhem 2 on Steam: https://store.steampowered.com/app/92...
Title: Rhem 2: The Cave
Release Date: Jun 2005
Developer: Knut Müller
Movement Style: Slideshow
Structure: Open
Item Usage: Low (contextual icons)
Isolation Level: High
Possible to die: No
Additional qualities: Atmosphere, intricate, complex puzzles, mechanisms, live actors
First time playing: No
Completed game: Yes
Used a guide: No
My rating: Strong Myst
For more info: https://notthefuture.com/mysty/
Solve this math puzzle for the longcut, enter the solution at: https://notthefuture.com/rewards/
Johnny has 1 apple which has 4 seeds inside. Johnny can plant the seeds to make an apple tree, but it takes years before it's able to bear fruit. Starting on the sixth year, the apple will grow ((y - 3)^2 - 5) apples per year, where y is the number of years since the tree was originally planted. This formula applies up until the tree bears exactly 1000 apples, after which it will yield 1000 apples each year until it dies at 100 (year 100 bears 1000 apples, 101 bears 0). Assume Johnny is able to consume as many apples as he wishes, and that each apple needs to be consumed to reach its 4 seeds, and also that each seed is planted and grows. How many apples will Johnny have eaten after the 20th year?
Fun fact: If Johnny started doing this the year the Declaration of Independence was signed, he would've eaten more apples than there are atoms in the universe by today.
Hint 1 below
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On the sixth year there is 1 full grown tree, and on the twelfth year there are 17 trees. After the sixth year, Johnny would have consumed 5 apples (the original and the 4 from year 6).
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Hint 2 below
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6: 1 tree, 4 apples (16 seeds), 5 total consumed
7: 1 tree, 11 apples (44 seeds), 16 total consumed
8: 1 tree, 20 apples (80 seeds), 36 total consumed
9: 1 tree, 31 apples (124 seeds), 67 total consumed
10: 1 tree, 44 apples (176 seeds), 111 total consumed
11: 1 tree, 59 apples (236 seeds), 170 total consumed
12: 17 trees (1 12y, 16 6y), 140 apples (76 + 64) (560 seeds), 310 total consumed
13: 61 trees (1 13y, 16 7y, 44 6y), 447 apples (95 + 176 + 176) (1788 seed), 757 total consumed
14: 141 trees (1 14y, 16 8y, 44 7y, 80 6y), 1240 apples (116 + 320 + 484 + 320), (4960 seeds), 1997 total consumed
15: 265 trees (1 15y, 16 9y, 44 8y, 80 7y, 124 6y), 2891 apples (139 + 496 + 880 + 880 + 496) (11564 seeds), 4888 total consumed
16: 441 trees (1 16y, 16 10y, 44 9y, 80 8y, 124 7y, 176 6y), 5900 apples (164 + 704 + 1364 + 1600 + 1364 + 704), (23600 seeds), 10788 total consumed
17: 677 trees (1 17y, 16 11y, 44 10y, 80 9y, 124 8y, 176 7y, 236 6y), 10911 apples (191 + 944 + 1936 + 2480 + 2480 + 1936 + 944) (43644 seeds), 21699 total consumed
18: 1237 trees (1 18y, 16 12y, 44 11y, 80 10y, 124 9y, 176 8y, 236 7y, 560 6y), 19757 apples (220 + 1216 + 2596 + 3520 + 3844 + 3520 + 2596 + 2240) (79028 seeds) 41451 total consumed
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Hint 3 below
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function appleSim(years)
{
var applesEaten = 1;
var treesByAge = [1];
for(var i=0; i[less than]years; i++)
{
var seedYield = 0;
var seedArr = [seedYield];
treesByAge = seedArr.concat(treesByAge);
var appleYield = 0;
for(var j=6; j[less than]treesByAge.length; j++)
{
if(treesByAge[j] [greater than] 0)
{
appleYield += treesByAge[j] * (Math.pow((j-3), 2) - 5);
}
}
applesEaten += appleYield;
seedYield = appleYield * 4;
treesByAge[0] = seedYield;
}
return applesEaten;
}
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