Thread: Math Problem #5

Help me please!!! Please explain me the easiest way to do this! Thanks!

Man Friday wrote down in a row several different positive integers less than 11. Robinson Crusoe examined these numbers and noticed with satisfaction that, in each pair of adjacent numbers, one of the numbers is divisible by the second one. At most how many numbers did Man Friday write down?

A) 6
B) 7
C) 8
D) 9
E) 10

6

9

4 8 1 5 10 2 6 3 9

Is there a way to do this with a system of equations?

It might help to make a table of 1-11, with what numbers they divide into as well as what numbers they are divided by. Looking at the 'divisible by' column, I thought of ways to assemble smaller sequences of numbers together into building blocks, and then tried to see how many of those building blocks I could put together without repeating numbers. I also ignored one since I know it connects to everything, and just saved it for connecting two chunks of building blocks that are unconnectable.

For example: I found that 6 can only have 2 and 3 with it, so I got {3,6,2}. also, 8 can only have a 2 and 4 with it, so there's {2,8,4}. Notice that you can connect these chunks at the 2 to form {3,6,2,8,4}. How could you make this chain bigger?

There are probably more efficient or rigorous ways to do it, but this seems kind of intuitive to me.