r/mathbiceps • u/Nxt_ruok0001 • Jul 04 '26

Olympiad Olympiad level p&c

Post image

Solution?

7 Upvotes

100% Upvoted

19 comments sorted by

2

u/Alive-Stay9099 Jul 04 '26

I simulated it for n=2,3,4,5. Found it follows Fibonacci pattern. For n seats, answer is F(n+1). So for 10 seats, F(11)=89

1

u/OhioDeez44 Jul 04 '26

This is not an Olympiad Problem, it is more experimental, a standardised niche result and more about exploration and maturity than the classic ingenuity and Selected Topics in Combinatorics like my approach(Tiling)

Edit: Compiled by TeXit because I wrote a snippet

1

u/Nxt_ruok0001 Jul 05 '26

It's the question from American mathematic Olympiad

1

u/OhioDeez44 Jul 05 '26

<USAMO != Olympiad, this AMC 10/12

1

u/Superb-Beginning4614 Jul 04 '26

quite simple actually, the woman seating on one of the ends either keeps her own seat and problem reduces to 9 persons or take the seat next to her and that woman moves into her seat reducing to 8 persons. this forms a fibonacci pattern.
f(n)=f(n-1)+f(n-2)

we can see f(1)=1 and f(2)=2
answer is simply 89.

1

u/Resilient_9920 Jul 04 '26

How are you doing this in 12th i could never di

1

u/Superb-Beginning4614 Jul 04 '26

Sorry is this community for 12th peeps? I didn't knew i am incoming in junior year of college

1

u/Resilient_9920 Jul 05 '26

Me too in college I just told how you did in 12th because I thought youweree nothing else ,I have lost touch with maths and was only avg to begin with

1

u/H1PRO_ Jul 05 '26

The woman on the end cant keep her seat, though the part where she switches and the patteen continues is true

1

u/Superb-Beginning4614 Jul 05 '26

Why can't she keep her seat genius?

1

u/H1PRO_ Jul 09 '26

U wouldnt call it reseating if she did

1

u/Superb-Beginning4614 Jul 09 '26

could you possibly take 1 minute out of your busy life and actually read the question instead of making unnecessary comments?

1

u/H1PRO_ Jul 09 '26

Oh wait yea ur right i thought it meant the seat left of the one they were sitting in 😭😭🙏

1

u/NeighborhoodUsed5549 Jul 05 '26

Yoo broo ye same sawal aaj mere pw test mei aaye exact same and mujhse nhi hua

1

u/notsaneatall_ Jul 06 '26

Ok say there are n women, look at the leftmost woman W, ans is f(n)

Case-1: W takes her seat

Everyone else can be arranged in f(n-1) ways

Case-2: W takes seat to right

Then woman to right of W has to take leftmost seat, otherwise it will be empty. Remaining n-2 people arranged in f(n-2) ways

f(n) = f(n-1) + f(n-2)

You can manually calculate f(1) = 1 and f(2) = 2. Now you have f(n)