Der Reis auf dem Schachbrett
(fast selbst berechnet... mit einem kleinen PHP-Skript)
Die Zahl der Reiskörner, die der Erfinder des Schachs für sich als Belohnung erbat, betrug:
18.446.744.073.709.551.615
Falls Du die Geschichte von der Erfindung des Schachspiels und der damit verbundenen Belohnung nicht kennst, dann betrachte die Zahlenkolonnen einfach als das was sie sind:
die Potenz von zwei bis 263 und deren Summe bis 264-1.
| Feld | Reiskörner auf diesem Feld | Summe der Reiskörner |
| 1 | 1 | 1 |
| 2 | 2 | 3 |
| 3 | 4 | 7 |
| 4 | 8 | 15 |
| 5 | 16 | 31 |
| 6 | 32 | 63 |
| 7 | 64 | 127 |
| 8 | 128 | 255 |
| 9 | 256 | 511 |
| 10 | 512 | 1.023 |
| 11 | 1.024 | 2.047 |
| 12 | 2.048 | 4.095 |
| 13 | 4.096 | 8.191 |
| 14 | 8.192 | 16.383 |
| 15 | 16.384 | 32.767 |
| 16 | 32.768 | 65.535 |
| 17 | 65.536 | 131.071 |
| 18 | 131.072 | 262.143 |
| 19 | 262.144 | 524.287 |
| 20 | 524.288 | 1.048.575 |
| 21 | 1.048.576 | 2.097.151 |
| 22 | 2.097.152 | 4.194.303 |
| 23 | 4.194.304 | 8.388.607 |
| 24 | 8.388.608 | 16.777.215 |
| 25 | 16.777.216 | 33.554.431 |
| 26 | 33.554.432 | 67.108.863 |
| 27 | 67.108.864 | 134.217.727 |
| 28 | 134.217.728 | 268.435.455 |
| 29 | 268.435.456 | 536.870.911 |
| 30 | 536.870.912 | 1.073.741.823 |
| 31 | 1.073.741.824 | 2.147.483.647 |
| 32 | 2.147.483.648 | 4.294.967.295 |
| 33 | 4.294.967.296 | 8.589.934.591 |
| 34 | 8.589.934.592 | 17.179.869.183 |
| 35 | 17.179.869.184 | 34.359.738.367 |
| 36 | 34.359.738.368 | 68.719.476.735 |
| 37 | 68.719.476.736 | 137.438.953.471 |
| 38 | 137.438.953.472 | 274.877.906.943 |
| 39 | 274.877.906.944 | 549.755.813.887 |
| 40 | 549.755.813.888 | 1.099.511.627.775 |
| 41 | 1.099.511.627.776 | 2.199.023.255.551 |
| 42 | 2.199.023.255.552 | 4.398.046.511.103 |
| 43 | 4.398.046.511.104 | 8.796.093.022.207 |
| 44 | 8.796.093.022.208 | 17.592.186.044.415 |
| 45 | 17.592.186.044.416 | 35.184.372.088.831 |
| 46 | 35.184.372.088.832 | 70.368.744.177.663 |
| 47 | 70.368.744.177.664 | 140.737.488.355.327 |
| 48 | 140.737.488.355.328 | 281.474.976.710.655 |
| 49 | 281.474.976.710.656 | 562.949.953.421.311 |
| 50 | 562.949.953.421.312 | 1.125.899.906.842.623 |
| 51 | 1.125.899.906.842.624 | 2.251.799.813.685.247 |
| 52 | 2.251.799.813.685.248 | 4.503.599.627.370.495 |
| 53 | 4.503.599.627.370.496 | 9.007.199.254.740.991 |
| 54 | 9.007.199.254.740.992 | 18.014.398.509.481.983 |
| 55 | 18.014.398.509.481.984 | 36.028.797.018.963.967 |
| 56 | 36.028.797.018.963.968 | 72.057.594.037.927.935 |
| 57 | 72.057.594.037.927.936 | 144.115.188.075.855.871 |
| 58 | 144.115.188.075.855.872 | 288.230.376.151.711.743 |
| 59 | 288.230.376.151.711.744 | 576.460.752.303.423.487 |
| 60 | 576.460.752.303.423.488 | 1.152.921.504.606.846.975 |
| 61 | 1.152.921.504.606.846.976 | 2.305.843.009.213.693.951 |
| 62 | 2.305.843.009.213.693.952 | 4.611.686.018.427.387.903 |
| 63 | 4.611.686.018.427.387.904 | 9.223.372.036.854.775.807 |
| 64 | 9.223.372.036.854.775.808 | 18.446.744.073.709.551.615 |
Den Code als Javascript zur Berechnung "beliebiger" Potenzen gibt's bei mir auf Gueldenstern-Webdesign.
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