The figures of the Hindus...
This one is from the book Liber Abaci, published in 1202. Authored by Leonardo Picano, as a compilation of all that he learned from his extensive travels, the book played a pivotal role in introducing Eastern knowledge into the (then) developing West. Because of the reputation of his father Bonacci (who was a state official), he sometimes took on the name of Leonardo Fibonacci (Fibonacci, from Latin Filius bonacci meaning the progeny of Bonacci). Eight hundred years later, only his last name stuck, and today he is known as Fibonacci.
The following puzzle from Fibonacci's book is a play on the "Hindu" decimal number system that he learnt in India:
"A group of people are seated in a row, and one of them is wearing a ring on a certain joint of a certain finger. One person, who knows the whereabouts of the ring, computes a number as follows: He finds the wearer's position in the row, multiplies it by x, adds 5, multiplies that by z, and adds p. Then, he adds a number indicating the finger, and multiplies this by q. Then, he adds a number indicating the joint. When this number is announced, it is easy to pinpoint the ring. "
Find x, z, p, q and tell me how to nail Frodo Baggins!
(*) The problem is not that hard. You can assume that the joints in each finger are numbered 1 to 4. Further, a particular solution will suffice but make sure that you state the crucial logic. As usual, the first solution gets a point. But there is a bonus for the most elegant solution!
The following puzzle from Fibonacci's book is a play on the "Hindu" decimal number system that he learnt in India:
"A group of people are seated in a row, and one of them is wearing a ring on a certain joint of a certain finger. One person, who knows the whereabouts of the ring, computes a number as follows: He finds the wearer's position in the row, multiplies it by x, adds 5, multiplies that by z, and adds p. Then, he adds a number indicating the finger, and multiplies this by q. Then, he adds a number indicating the joint. When this number is announced, it is easy to pinpoint the ring. "
Find x, z, p, q and tell me how to nail Frodo Baggins!
(*) The problem is not that hard. You can assume that the joints in each finger are numbered 1 to 4. Further, a particular solution will suffice but make sure that you state the crucial logic. As usual, the first solution gets a point. But there is a bonus for the most elegant solution!
posted by littlecow at 12/07/2005 08:13:00 PM
3 Comments:
@arete: welcome! homerun on first pitch. but really, the beauty is in finding out 'why' your solution works (and that is the crux of the "hindu decimal system"!)
saami, if the dude knows the position of the ring and expresses it as 3 digit number using powers of 10, how different is it from the dude revealing the position, finger and joint as three separate numbers. maybe i didn't understand the problem, but what is the value in doing all these calculations ? i will just multiply the row position by 100, finger position by 10 and joint position by 1 and add, or just say the three numbers directly.
@lenscrafter: thats the whole point of it. while it seems trivial to us now to express numbers by having 'place values' for the digits, it was not a common practice until the 'hindus' came up with this idea! and europeans learnt about it less than 800 years ago. admittedly, this was an easy puzzle. fret not, the next come will come up real soon!
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