Select flag then space to walk through the squares. Select 1 for an example of size. Then 2 to go to next examples. Python code to simulate the same: total = 1 square = 1 print "1: 1 grain." for n in range(63): total = total * 2 square = square + 1 print str(square) + ": " + str(total) + " grains." total = 10 square = 1 for n in range(63): total = total + 10 square = square + 1 print str(square) + ": " + str(total) + " coins."
While you are eating snack today, I will tell a quick story. At the end of the story I will tell you how to start with an allowance of one penny and get very rich within a few months. Remind me at the end. This is an old story - probably from Persia but some version of it is told in many parts of the world. A young girl - lets call her Lola - lives in a small village in a large kingdom. Her village works very hard each year to make sure they have enough rice to feed the village. In a good year they have just enough. During the rainy season they cannot work in the fields so they play chess, a game which is popular across the whole kingdom. Lola is really good a chess. At first she beats her peers in the village, then the adults. She becomes famous in the area and people from other villages come to play her. Most of the time she wins. The prince in the capital hears about Lola's skill. At the beginning of one rainy season he invites her to the castle. To pass the time they will play 64 games of chess - one for each square on the chess board. For each game Lola wins she will get 10 gold coins. An enormous amount of money! 5 gold coins could feed her family for a year. If she won even a few games she would be the richest person in her village. Lola thanks the prince for the generous offer. But she then asks for a different prize for winning. "If I win 1 game, please give me a single grain of rice. For every game I win after that please double the amount of rice." The prince is puzzled. He wonders if Lola is really so smart as people say. Rice instead of Gold? And such a small amount to start? After 2 wins she gets 2 grains; after 3 wins she gets 4 grains; the 4th win 8 grains; then 16; then 32 ... After 6 wins she would have 60 gold pieces - but she is asking for a spoonful of rice? Lola insists and they play. She wins - not every game but most of them. [Discuss hit "flag" then space to walk through squares] [ select "1" to go to first - "2" for each following example ] At 20 wins she has a nice bag of rice. By 28 wins the rice would fill a room like this. Win 32 it would fill this entire hall. At 36 or so the rice would fill this building. Somewhere around 40 wins the weight of the rice would burst the bags. If she got to 48 wins, Hoboken would be covered in rice a few inches thick. It would look like a snowstorm blanketing from the city. This was more rice than the entire kingdon grew in a year - more than the entire world grew. An impossible amount of rice. But the prince made this promise, he would make sure that every village had enough rice to get through the winter as long as he lived. Lola became a celebrated chess champion and lived a long happy life. COINS 1: 10 coins. 2: 20 coins. 3: 30 coins. 4: 40 coins. 5: 50 coins. ... 35: 350 coins. 36: 360 coins. 37: 370 coins. 38: 380 coins. 39: 390 coins. 40: 400 coins. 41: 410 coins. 42: 420 coins. 43: 430 coins. 44: 440 coins. 45: 450 coins. 46: 460 coins. 47: 470 coins. 48: 480 coins. 49: 490 coins. 50: 500 coins. 51: 510 coins. 52: 520 coins. 53: 530 coins. 54: 540 coins. 55: 550 coins. 56: 560 coins. 57: 570 coins. 58: 580 coins. 59: 590 coins. 60: 600 coins. 61: 610 coins. 62: 620 coins. 63: 630 coins. 64: 640 coins. RICE 1: 1 grain. 2: 2 grains. 3: 4 grains. 4: 8 grains. 5: 16 grains. 6: 32 grains. 7: 64 grains. 8: 128 grains. 9: 256 grains. 10: 512 grains. 11: 1024 grains. 12: 2048 grains. 13: 4096 grains. 14: 8192 grains. 15: 16384 grains. 16: 32768 grains. 17: 65536 grains. 18: 131072 grains. 19: 262144 grains. 20: 524288 grains. 21: 1048576 grains. # 1 million (6 digit) 22: 2097152 grains. 23: 4194304 grains. 24: 8388608 grains. 25: 16777216 grains. 26: 33554432 grains. 27: 67108864 grains. 28: 134217728 grains. 29: 268435456 grains. 30: 536870912 grains. 31: 1073741824 grains. # 1 billion (9 digit) 32: 2147483648 grains. 33: 4294967296 grains. 34: 8589934592 grains. 35: 17179869184 grains. 36: 34359738368 grains. 37: 68719476736 grains. 38: 137438953472 grains. 39: 274877906944 grains. 40: 549755813888 grains. 41: 1099511627776 grains. # 1 trillion (12 digit) 42: 2199023255552 grains. 43: 4398046511104 grains. 44: 8796093022208 grains. 45: 17592186044416 grains. 46: 35184372088832 grains. 47: 70368744177664 grains. 48: 140737488355328 grains. 49: 281474976710656 grains. 50: 562949953421312 grains. 51: 1125899906842624 grains. # 1 ? (15 digit) 52: 2251799813685248 grains. 53: 4503599627370496 grains. 54: 9007199254740992 grains. 55: 18014398509481984 grains. ... 61: 1152921504606846976 grains. # 1 ? (18 digit) 62: 2305843009213693952 grains. 63: 4611686018427387904 grains. 64: 9223372036854775808 grains.
