Unrealized reward
According to legend, chess was invented by Sass Bandal, the prime minister of ancient India. She Hanwang also liked playing chess very much at that time. One day, when the king was playing chess with Doyle, he said to him, "If you win, what reward do you hope to get?" Dahl said, "I hope your majesty will give me rice." The king smiled: "How much do you want?" Dahl said, "Please ask your Majesty to have the rice grains put on the chessboard, the first grid 1 grain, the second grid with 2 grains, the third grid with 4 grains, and the fourth grid with 8 grains ... So the latter grid is put down according to the rule of twice the previous grid until the last grid."
The king thought, "A small chessboard has only 64 squares. How many grains of rice can you put down? " I readily agreed.
If you think so, you are all wet. If you don't believe me, let's do the math.
The first cell is 1 capsule, the second cell is 2 capsules, the third cell is (2×2) capsules, marked as 22, the fourth cell is (2×2×2), marked as 23 ... The last cell is 263 capsules, and the total is:
1+2+22+23+...+263 =1844674073709551615 (grain).
Calculated by 1 cubic meter of rice, it is about1500 million grains, which is equivalent to about1200 million cubic meters. It is impossible for the world to produce so much food in 2000!
After the above calculation, you must understand that this is an unrealized reward.
Origami is higher than the mountain.
In our life, there are many things and phenomena, and it is hard to imagine their results without "mathematical processing".
For example: an ordinary newspaper, fold in half, fold again, fold again ... how high can you fold it 30 times?
This thing seems simple, but in fact it is very difficult to "operate" in reality. Let's do the math.
Suppose the thickness of the newspaper is 0.01mm. After the first folding, the height is 0.01× 2 = 0.02 (mm); After the second folding, the height is 0.0 1×22=0.04 (mm) ... and so on, the height of the paper after 30 folds is:
0.0 1×230=0.0 1× 107374 1824=
107374 18.24mm≈ 10737m。
Wow! It is really an "origami mountain". After a newspaper is folded in half for 30 times, it is much higher than Mount Everest.
The speed of spreading rumors is amazing.
After someone heard the rumor, he passed it on to two people within an hour, and then he stopped passing it on to others; And those two people also passed it on to the other two people within an hour, and then they stopped passing it on to others ... So, can it spread all over a big city with a population of10 million overnight?
Please note that in an hour, one person will only pass it on to two people, and there are only 24 hours a day and night. Is it possible to spread all over a big city with a population of10 million?
It is difficult to make a correct judgment by intuition alone. The most reliable way to get the answer is to calculate:
1 hour, passed to 2 people;
The second hour, to 22 = 4 (people);
The third hour, to 23 = 8 (person);
At the 4th hour, it reached 24 = 16 (person);
……
At the 23rd hour, it reached 223 = 8388608 (person);
At the 24th hour, it was sent to 224 = 1677 72 16 (person).
In other words, it can be distributed to 167772 16 people in the last hour. Therefore, if the ideal conditions are met, it is absolutely no problem for rumors to spread to a big city with a population of10 million overnight. How amazing the spread speed of this rumor is!
Students, after reading these three stories, do you know the power of power operation? Then explore its mystery in future study.