Hmmm... seems to me that the picture is of himself. Not positive, but that is the best that I can come up with. The solution says it is his son. I am not sure about that. However, if the picture was of the man himself, I think that fufills the requirements of the riddle?
An alternative method would be to use proportions (it is the same thing as post #2 just in a different form).
38, "a" is what percent of 216, "b"? :
First write your two numbers as a fraction: 38/216.
Now, a percent is what fraction of 100 a number is, so you can write what percent 38 is of 216 as a fraction: x (whatever percent of 216 38 is)/100
So now you have: x/100.
So 38 is the same ratio to 216 as x is to 100 so you can set the two expressions equal: 38/216 = x/100.
Now you solve the equation:
38/216 = x/100
17.5925... = (1)x
So, 38 is approximately 17.5926% of 216.
If you wish, you can check your answer.
Take your percent (17.5926) and divide it by 100: 17.5926/100 = .175926
Now multiply this number by the denominator of your other fraction (that is "b" in the expression "find the percent a of b"), so in this instance we would have (.175926)(216).
If you set your proportion up correctly, this should equal "a" :
This is 0.000016 different than what you should get. This error is due to rounding, if you carried the decimals in 17.5925... to infinity, then you would get exactly 38.
Since 38 = a, the solution "checks".
More generally, if you wish to know what percent, "x", "a" is of "b", then just set up and solve the proportion : a/b = x/100.
x will be your answer.
I have read a little about busy beaver functions, but I do not really understand how they work. I know it has to do with the number of steps Turing machines will run until they halt, but I do not understand where the answers come from!? What calculations are being performed? Also, why do the numbers grow so large so quickly? Can this be explained so that it is easy to understand? Thanks.
Well, if all that is already on the island what is the purpose of burning the entire island? I could understand burning a plot of land to make a garden, but not the entire island. Wouldn't you potentially be destroying lots of potentially useful resources? Is there some reason why you cannot make a garden without burning the island down?