These are the answers to the puzzles posted in the online puzzle series on the official website of Techfest 2008,IIT Bombay
dx ia dfa iapd bxe fhka dx iahd dfa iapd
to be the best you have to beat the best
2. WHO IS THE MONKEY
Every sailor leaves 4/5(n-1) coconuts of a pile of n coconuts. This results in an awful formula for the complete process (because every time one coconut must be taken away to make the pile divisible by 5): 4/5(4/5(4/5(4/5(4/5(4/5(p-1)-1)-1)-1)-1)-1), where p is the number of coconuts in the original pile, must be a whole number. The trick is to make the number of coconuts in the pile divisible by 5, by adding 4 coconuts. This is possible because you can take away those 4 coconuts again after taking away one fifth part of the pile: normally, 4/5(n-1) coconuts are left of a pile of n coconuts; now 4/5(n+4)=4/5(n-1)+4 coconuts are left of a pile of n+4 coconuts. And because of this, the number of coconuts in the pile stays divisible by 5 during the whole process. So we are now looking for a p for which the following holds: 4/5×4/5×4/5×4/5×4/5×4/5×(p+4)=(46/56)×(p+4), where p is the number of coconuts in the original pile, must be a whole number. The smallest (p+4) for which the above holds, is 56. So there were p=56-4=15621 coconuts in the original pile.
This is an easy question
The correct answer is 4.
4. INDIAN COLONY
try to google for zebra puzzle
2. abcdef = 142857. Note that a = 1 immediately from the first equation. Incidentally, 142857 is the only number known to have this cyclic property.