I am a three digit number.
I am either divisible by 3 or by 5.
I am either divisible by 4 or by 6.
I am either divisible by 5 or by 7.
I am either divisible by 6 or by 8.
I am either divisible by 7 or by 9.
I am either divisible by 9 or by 11.
What am I?
(Note: "divisible" means leaving no remainder.)
Well, a three digit number that fulfills the series of conditions above is 462 or, written differently, the number whose decomposition leads to the following:
462 = 2.3.7.11
My line of reasoning was guided through a few basic instructions, such as: if a number's decomposition lead to both 3 and 5 factors, whatever the number was wouldn't fulfill the first sentence, and so on.
Thus, the decomposition above will only correspond to one given condition for each pair, and I believe this is one valid solution for this problem. However, a more mathematically labored answer shall provide the answer for whether the problems can be fulfilled by additional answers or not, even though I believe it won't.
A solution, perhaps?
