Retreat has been pretty fun so far. Hanging out with APhiO and especially with Toy Class is always awesome.
I jus twanted to make a quick post about my math problem from She-Ra. The girls had included one in the last He-Man, but it was something pretty simple that you should be able to do in your head, so I stepped it up a notch.
Known as the “Wheat and Chess Board” problem, it’s been told a lot of different ways, but it usually goes something like this:
“When the creator of the game of chess showed his invention to the ruler of the country, the ruler was so pleased that he gave the inventor the right to name his prize for the invention. The man, who was very wise, asked the king this: that for the first square of the chess board, he would receive one grain of wheat, two for the second one, four on the third one and so forth, doubling the amount each time. The ruler, who was not strong in math, quickly accepted the inventor’s offer, even getting offended by his perceived notion that the inventor was asking for such a low price…”
How many grains of wheat did the inventor ask for?
For She-Ra, the challenge was not in getting the answer itself, but in finding the fastest way to get the answer, because the three teams had to race each other to find it, with an overall deadline of ten minutes.
To find out what the best method (and answer) is, click on the Show ▼
The answer is 18,446,744,073,709,551,615 grains of wheat. But how do you find that within ten minutes?
The answer can be found by using “brute force,” or just adding up each chess square’s value. It would be 1 + 2 + 4 + 8 + … until you had added up 64 numbers to account for the 64 squares on the chess board. Another way to write those addends is as 20 + 21 + 22 + … + 263.
If you think of those same terms in binary, it would 1 + 10 + 100 + 1000 + … + 1000000000000000000000000000000000000000000000000000000000000000, or 1111111111111111111111111111111111111111111111111111111111111111, which is just one less than 10000000000000000000000000000000000000000000000000000000000000000.
So the fastest way to find the answer would be to find 264 and then subtract one from it.
Oh, and in case you missed She-Ra, none of the teams used the strategy I suggested. They all tried to use brute force in base 10. Then, as the ten minute limit approached, they all tried to guesstimate the answer.
Loose family actually turned in a Riemann sum of the powers of 2 from 0 to 63. While technically correct, I had asked for the answer in plain number form, so I couldn’t give them credit. Tight family, led by Mika (from whom I expected better) and Rachel, turned in 9 x 1020. And Close family was “led” by Mimi, who supposed just put a 1 and a random number of 0s after it, and that number happened to be 20.
So Close family won that round by sheer luck. 
Tags: Family
aw, loose…
it’s hard to think under pressure. i’m pretty sure i’ve heard this one before but i wouldn’t have remembered the easy way to do it.
And that is why we are the awesome!