Valuable coins kept by the Treasury at Fort Knox are stored in sealed identical chests. Each chest has two compartments, filled with equal amounts of gold coins and equal amounts of silver coins (but numbers of gold and silver coins are different).
According to the books kept by the Treasury there should be 500,000,000 chests. But, alas, only according to the books. The audit revealed, that despite all inspected chests remained properly sealed, total amount of coins in all chests are:
327160698919750151 gold coins, and
981482103259250362 silver coins.
Apparently someone stole several chests full of coins.
2007-12-06 05:47:29 · 3 answers · asked by Alexander 6 in Science & Mathematics ➔ Mathematics
If N chests have been stolen, each with one compartment of gold coins and one of silver, then the remaining number of gold coins is (500,000,000 - N) * X and of silver coins is (500,000,000 - N) * Y, where X and Y are the number of gold and silver coins in each compartment.
There are methods of finding the "greatest common divisor" of the two huge numbers in the problem without actually factoring either of them. The method finds that they are both exact multiples of 499,999,993, therefore 7 chests of coins have been stolen. This number of chests remaining happens to be a prime number, but the method of finding it would work for either a prime or a composite common divisor.
Although it was not part of the question, we can find by dividing that there are 654,321,407 gold coins and 1,962,964,234 silver coins in each compartment. The gold number is prime, and the silver number is 2 * 7 * 11 * 12,746,521.
2007-12-06 06:14:28 · answer #1 · answered by Anonymous · 4⤊ 0⤋
If I am calculating correctly there is only 3 left of the 500,000,000 chests leaving a total of 499,999,997 stolen?
2007-12-06 14:10:45 · answer #2 · answered by Red 2 · 0⤊ 2⤋
I dont know but it wasn't me. I just got here.
2007-12-06 13:50:18 · answer #3 · answered by clavdivs 4 · 2⤊ 1⤋