One quiz at a time

[Doggett]

Right ankle?

[PhilW]

Right ankle?

Best Western?

[flash_uk]

Right ankle?

Best Western?

Nope.

[Doggett]

Marriott?

[PhilW]

I can’t yet see what is the optimal guessing strategy.

Instinct suggests to me to halve the space, once a range is determined, by guessing half-way outside the known range.

To define the search space initially requires a minimum of three guesses, where the middle guess is the best (i.e. we require the best guess plus at least one either side of it). For example, A,B,C where A < B < C and B is closest; for sake of argument in this case, A is second, C is third.

Therefore:
B-X < X-A => X > (B+A)/2
X-A < C-X => X < (C+A)/2

This provides the initial bounds for a known range (essentially using the half-way position between each pair of the top two guesses). This can be halved with each subsequent guess, by guessing a half-range distance outside the known range in the opposite direction from second best. In this case therefore, the next guess would be:

D = Upper bound (since 2nd best is lower) + half range
D = (C+A)/2 + ( (C+A)/2 - (B+A)/2 )
D = (2C+A-B)/2

The order of guesses from best to worst will now either be BDA or BAD, in either case determining the upper or lower half of the previous range as the new valid range.

Notes:
- Additional points previously guessed outside this range provide no additional data (unless they already provided it previously and there has been redundancy in the later (and best) guesses.
- Guessing within the range can provide better or worse information than the 50% reduction strategy above. The reduction by guessing in the range *might* be a normal distribution depending on X, B and D, but seems to me more likely that the mean reduction in range would be less than 50%, based on perception of likelihood of being being proportionately more likely to be near the centre of the range, and then the reduction in range to be from half-way between B and new guess to the other limit end most of the time. If true, then the above halving strategy would be superior to guessing in the range, at least until the range is small enough that the chance of correct guess skews the probability for range reduction.

[PhilW]

Novotel/Sofitel ?

[Old Bridge]

2830

A lucky guess or a brilliant deductive power?
Well done.

[Old Bridge]

Hilton Hotels

[PhilW]

Premier Inn?

[Old Bridge]

Radisson

[PhilW]

Four pillars?

[Old Bridge]

Doubletree

[flash_uk]

2830

A lucky guess or a brilliant deductive power?
Well done.

Was employing the halfway point (roughly) in the range strategy!

[flash_uk]

Radisson

Yes indeed, it was the Radisson Blu in Belfast. Your question.

[Old Bridge]

Rock and roll.
Port.
Find the one word I'm thinking connects the two very well.

[Doggett]

Berry

[Old Bridge]

Berry

Brilliant! (Or too easy)
Your question Doggett.

[Doggett]

Brilliant! (Or too easy)

Let's go with brilliant

The question is:

How many many founding members were there of the Oporto British Club in May 1903, having paid £22 (100 milreis) each?

[flash_uk]

22

[jdaw1]

108?

[Doggett]

Mike is closest so far...

[jdaw1]

But the best guess can be irrelevant. Consider 24 is the best; 12 is second; 30 is third; and 8 is fourth.

[Doggett]

But the best guess can be irrelevant. Consider 24 is the best; 12 is second; 30 is third; and 8 is fourth.

Mike is still the closest. If there is another guess then Phil's logic may then be applied and tested.

[PhilW]

6

[PhilW]

But the best guess can be irrelevant. Consider 24 is the best; 12 is second; 30 is third; and 8 is fourth.

Correct, but only at the time range is first established, or in the case of non-optimal guesses following range establishment. In some cases it would be possible when range is first established, to tighten that range based on previous guesses, and then proceed optimally. In others it may be that a non optimal guess may have been made after the range was established. You example could either of those cases depending on order of the guesses.