Puzzles with numbers and things

[davis_greatest]

Breaking News - Hall Of Fame

Due to concerns about bankruptcy and the risk that I may be needing to finance the award of 1, 2 or perhaps even as many as 3 bananas within the next year or two, and to celebrate the fact that we reached 100 questions, I am going to try a little change. I am going to try continuing this thread with puzzles but no points! So, everyone can have a go, but the reward will be only fame.

Therefore, instead of a Scoreboard, there will be a Puzzles with numbers and things Hall of Fame. As soon as someone gets a question correct, that ape (or person) will be eligible for entry to this illustrious Hall of Fame.

Here then, in no particular order (for there is no order), is the latest Puzzles with numbers and things Hall of Fame

Oliver (my pet orang-utan)
Gordon (my pet gorilla)
Charlie (my pet chimpanzee)
snookersfun
abextra
davis_greatest (Oliver's, Gordon's and Charlie's pet something)
Vidas
chasmmi
elvaago
robert602
Sarmu
The Statman
austrian_girl
austrian_girl's dad
Semih_Sayginer
Snooker Rocks!
Ginger_Freak
April Madness

[davis_greatest]

Round 101 - Primate Egg Cricket

Here is a great chance for a new entrant to get in the Hall of Fame (but anyone can answer)!

At 5pm today, Charlie opened my wallet and took out an infinite amount of money. He then went to my local supermarket and bought an infinite supply of eggs.

At 5.50pm today, he will go to his friend Barry The Baboon, and they will have a game of Primate Egg Cricket. Charlie bowls, and Barry is in to bat. The game is played as follows:

Charlie bowls his eggs to Barry, who swipes at them with his tail. Each time, Barry has:

- a 20% of hitting the egg with his tail, in which case the egg will be swiped back towards Charlie; and
- an 80% chance of missing the egg completely, in which case the egg will land harmlessly on the the goose feathers behind Barry.

If Barry hits the egg, then:

- Charlie has a 50% chance of catching it; and
- there is a 50% chance that Charlie will miss it and it will smash on his face.

At 6pm, Charlie will bowl the first of his eggs. Each egg takes one second to travel from Charlie to Barry and, if Barry successfully hits the egg with his tail, it takes another second to travel back to Charlie. Charlie bowls the eggs 10 seconds apart (so would bowl at 6:00:00, 6:00 and 10 seconds, 6:00 and 20 seconds etc).

The game continues until Charlie gets egg on his face.

What is the expected time at which the game ends?

Answers on the thread please!

[abextra]

I'm sure it will take at least two seconds before the egg smashes on Charlie's face.

[davis_greatest]

I'm sure it will take at least two seconds before Charlie's face gets smashed by the egg...Maybe 6:01:42?

Hehehe Yes, at least 2 seconds... but what is the expected time?

PS Charlie's face doesn't get smashed - just rather messy - the egg gets smashed...

[davis_greatest]

PPS There have been 3 attempts at this question so far (none right yet ), but no one has dared openly post an answer on this thread. Why the shyness in posting here? Are you all afraid of getting egg on your face?

[snookersfun]

Because it is probability. Ok, what the....
let's go for 6:01 and 32 sec

[rambon]

Well the highest probability is 6:00:02, but that's not the question, it's expected.

I would say 6:00:42 would be the expected time, but then that's far from a fully calculated answer

[elvaago]

Start. Egg is thrown. Chances of it being missed are 80%. Chances of it being hit are 20%. If it gets hit, then the chances of it being missed is 50%. So 50% * 20% = 10%. This is the chance of the game being done after the first round (where one round is a throw, a return hit and a miss.)
So the chance of the game not being done is either it gets missed after the first throw (80%) or it gets hit and then caught (20%*50%) is 90%.

Second round.
Same math applies times 90%.
So the chance of an end of the game is 9%, leaves 81% for the game to continue.

Third round. 8.1% for an end, 72.9% for a continuation.

Etc.

So I think the game is expected when 10+9+8.1 + etc is higher than 50%, which is after 7 throws. 2 + 6 * 12 = 74 so I expect it to be over at 6:01:14

I think the match is guaranteed to be over after 160 rounds or 2 + 159 * 12 =1910 seconds or at 06:31:50.

Those are my two cents, however wrong they might be. I don't mind a bit of egg in my face!

[rambon]

The answer has to end in either 02, 12, 22, 32, 42, 52 seconds, as the throw is every 110 seconds, not ten seconds after the 2 seconds for the egg's journey have elapsed....

Can I have a point for that bit at least...?

[elvaago]

You're right. I'm chancing my answer to 6:01:02. :-D

[chasmmi]

6:01:22 fyi

[davis_greatest]

Congratulations snookersfun

Some good answers & attempts both on the thread and by PM from snookersfun, abextra, rambon and elvaago!

No points for anyone are up for grabs - only places in the Hall of Fame, and you are all in it already!

snookersfun's (final ) answer of 6:01:32 is correct!

The probability that any particular egg hits Charlie's face is 20% x 50% = 10% = 1/10.

So the expected number of eggs bowled until the game is over is 10.

The first egg (if hit) would arrive back at Charlie 2 seconds after 6pm. So the 10th egg would arrive back 92 seconds after 6pm. That's 6:01:32.

[davis_greatest]

I think the match is guaranteed to be over after 160 rounds or 2 + 159 * 12 =1910 seconds or at 06:31:50.

Those are my two cents, however wrong they might be. I don't mind a bit of egg in my face!

Nice start - went a bit off track when you got to the 50% chance of being over ... no egg on your face though

At no finite time is the match guaranteed to be over - Barry could have kept missing with his tail!

[rambon]

Nice start - went a bit off track when you got to the 50% chance of being over ... no egg on your face though

At no finite time is the match guaranteed to be over - Barry could have kept missing with his tail!

And if he's English he probably will...

[davis_greatest]

And if he's English he probably will...

Hehe

The answer has to end in either 02, 12, 22, 32, 42, 52 seconds, as the throw is every 110 seconds, not ten seconds after the 2 seconds for the egg's journey have elapsed....

Can I have a point for that bit at least...?

Incidentally, although the answer does end in 2 seconds, this does not have to be the case for the reason you gave. If, for instance, there had been a 50% chance that the game ended at 6:00:02 and a 50% chance that it ended at 6:00:12, then the expected time of ending would be halfway between, so 6:00:07, which does not end in 2