Rog's Rag-bag

Maths, logic, trivia, puns, general silliness - an assortment of stuff too disparate to go under any other title. In other words, same old rubbish...

-1. What number should replace the question mark and why?

-2. Four people are seated waiting for their Covid vaccination. Mrs Brown is next to Mrs Green but not next to Mr Jones. Mr Jones is not next to Mr Gill. Who is next to Mr Gill?

-3. What is the next number in the following sequence?:
212
223
242
526
272
829

-4. “As a kid I was made to walk the plank. We couldn’t afford - ---".

-5. A ball is dropped to the ground from a height of 10 feet. It then bounces back up to half its original height and falls back. It repeats this, always bouncing up half of the previous height. If the ball bounces an infinite number of times before coming to rest, how far does it travel?

-6. “I've just seen a documentary on how ships are held together. R-------!”

-7. A rebus:
PERSON
PERSONS
PERSONS
PERSONS

-8. The late Phil Spector made his debut in the pop world in 1958 as part of which vocal trio?

-9. What musical term is indicates a chord where the notes are played one after another rather than all together?

-10. This is a (disguised) still from the end of which film?

8. The Teddy Bears

6. Riveting. You're a funny man Rog.(lol)

7. first person singular

10. Casablanca

Gentlemen - I salute you!

5. 10 feet

Oops - missed a couple there. michele , fil also good calls!

Afraid it doesn't match mine , young Sue. It's already done 15 on the first bounce (10 down and 5 up)

1. 4 because the numbers correspond to the amount of lines needed to create the letters

Nice one, jb - thought that might last a bit longer!

Ok, Rog, I figured that if the ball stays within 10 feet, that's the distance traveled. But you want the distance traveled within that 10 feet so the answer is infinity because the bounces will never stop.

10 +5+5 +2.5+2.5+1.25 +.....

2. Mrs Brown

You got it, oldbroad!

That's it, Sue. It's made up of two series, one going 10, 5, 2.5... (the "downs") and the other going 5, 2.5, 1.25... (the "ups"). I think there is a mathamatical formula (which I can't remember!) that gives you the total distance after an infinite number of bounces, but if you add them up by hand for the first 5 or 6 bounces (and maybe plot them on squared paper) you should get a good idea of what they'll finish up at...

I made the mistake of looking for the formula. There IS one because what's been proven is:

"Mathematically, we have to use the fact that (for some cases) the sum of an infinite number of terms is a finite number."

a = initial height of drop = 10
r = percentage of bounce back (1/2)

2(a/1-r) - a
2(10/.5) - 10
2(20) - 10
30

Another site suggests the 50% bounce back doesn't stay consistent. Their formula is more daunting.

3. 303

Very tricky putting them in a column, Rog! It's much easier to see when you write them out in a line.

They both look good to me, ladies!

That was going to be the hint, Cheryl

4. a dog?

Yes - I quite liked that one Lex

9. Arpeggio

Hi Rog.

Hi Remi - nice finish!