Logic Q

[Amina-DZ]

For a maximum number of inhabitants n + 1, the maximum number of hairs should be n, which is true if there are people with hairs from 0 to n. But since 518 is not permitted, for any maximum number of inhabitants, n > 518 , the maximum inhabitants possible is only n,
Hence the maximum inhabitants possible is 518.

E.g. if we consider 519 or more inhabitants, then inhabitants 1 through 518 could have 0 through 518 hairs but the 519th cannot have 518 hairs (this breaks rule 2). That inhabitant would have to have either 519 or more hairs (which breaks rule 3) or some other number that is equal to that of another inhabitant (which breaks rule 1).

P.S. I can only apologise for what I wrote yesterday lol it's amazing what a good night sleep does to our brain!!

[Amina-DZ]

Originally posted by Shotokan_Karate

Ah! More puzzles in my absence huh!

Oh dear cara rivale! this seems so easy!

I know

Gosh you just beat me to it, I was posting my reply! I don't know what happened to me yesterday!! I was laughing at myself this morning

[phylay]

Shotokan, I warned I was starting with easy ones
Amina, you worried me yesterday and I nearly had a doubt on my solution . Which mean were u using if not your brain

Next one this evening when I get home

[Shotokan_Karate]

Oh! I'm gonna miss more! OK, here's another one for now to get that brain working as it should


The diagram shows a regular pentagram:



What is the ratio of AB to BC?

[Amina-DZ]

Need to find the ratio: b/d

b/a = a/c (using the 2 corresponding triangles)

but:
c = 2b+d
a = b+d

b/(b+d) = (b+d)/(2b+d)
2(b^2) + bd = (b+d)^2
b^2 = d^2 + bd
b/d = (b^2 - d^2)/d^2
b/d = (b/d)^2 - 1

I'm turning in circles

[Amina-DZ]

Originally posted by phylay
Amina, you worried me yesterday and I nearly had a doubt on my solution . Which mean were u using if not your brain

what else would I be using? At least I thought I was using my brain, but I was tired so it wasn't 100% active

[phylay]

Originally posted by Amina-DZ



Need to find the ratio: b/d

b/a = a/c (using the 2 corresponding triangles)

but:
c = 2b+d
a = b+d

b/(b+d) = (b+d)/(2b+d)
2(b^2) + bd = (b+d)^2
b^2 = d^2 + bd
b/d = (b^2 - d^2)/d^2
b/d = (b/d)^2 - 1

I'm turning in circles

Lol,
I am leaving my office now... I'll start thinking when I get home and after a small rest. This gives you more than 1h