Puzzles with numbers and things

[moglet]

R383

I have 15 lucky ladies.

[davis_greatest]

At least 13.

I have 15 lucky ladies.

Congratulations to both abextra and moglet.

It looks like abextra but not moglet is online right now, so abextra, please put yours up. Then hopefully moglet can add any extra ones (unless abextra has more than 13 now, in which case they can all go up. )

[abextra]

9 x 10p

20p + 6 x 10p
2 x 20p + 3 x 10p + 4 x 5p
3 x 20p + 6 x 5p
3 x 20p + 2 x 10p + 5p + 2 x 2p + 1p
4 x 20p + 5 x 2p
4 x 20p + 5p + 2p + 3 x 1p

50p + 8 x 5p
50p + 2 x 10p + 3 x 5p + 2 x 2p + 1p
50p + 3 x 10p + 5 x 2p
50p + 3 x 10p + 5p + 2p + 3 x 1p
50p + 20p + 10p + 5 x 1p
50p + 20p + 10p + 4 x 2p + 2 x 1p
50p + 20p + 2 x 5p + 5 x 2p
50p + 20p + 3 x 5p + 2p + 3 x 1p

Hope it works for 15 roses.

[davis_greatest]

20p + 6 x 10p
50p + 20p + 10p + 5 x 1p

Thanks abextra. It looks like these haven't pasted in properly...

[abextra]

Thanks abextra. It looks like these haven't pasted in properly...
20p + 6 x 10p
50p + 20p + 10p + 5 x 1p

ohh...

20p + 6 x 10p + 2 x 5p
50p + 20p + 10p + 5p + 5 x 1p

sorry, hope it's better now!

[davis_greatest]

I think we can take it that all solvers found the 15 lucky ladies- well done! - which means on to...

Round 384 - He's gone bananas!

Charlie, Oliver and Gordon are off to visit Barry the Baboon's Ball Shop, in the hope of getting a practice cue ball each.

"Listen," says Oliver before they leave my home. "I heard that Barry is running a special offer, which is that if you give Barry a number of bananas when you enter his shop, then he will bring out from his storeroom to the cashdesk some piles of crates. The number of piles will equal the number of bananas you give him. The number of crates in each pile is also that same number of bananas you give him. And, each crate contains a number of white balls equal to that same number of bananas!"

"What Barry said he will then do," continues Oliver, "is carry one of the crates back to the storeroom (I really don't know why he had to bring it out in the first place), before he comes back to the cashdesk to open the remaining crates and take out all the balls. He will then paint, as far as possible, equal numbers of balls yellow, green, brown, blue, pink and black, for him to sell. However, any white balls remaining (which could be up to five, I suppose), he will then give away!"

"Well," says Charlie, "we've got a huge stock of unneeded bananas right now. Let's choose a number of bananas to get the most possible "free" white balls we can!"

How many white balls do my apes get from clever Barry?

Answers by Private Message please...

[davis_greatest]

sorry, hope it's better now!

Yes, looks perfect!

[abextra]

Round 384 - He's gone bananas!

Charlie, Oliver and Gordon are off to visit Barry the Baboon's Ball Shop...

Lol, what a wonderful question again - I like it so much - THANK YOU!!!

You really know a lot about numbers!

[davis_greatest]

Congratulations to abextra, Monique, moglet and snookersfun, all of whom have successfully solved round 384! Well done

Please would someone now put the answer up on the thread - either one of these four or if there is anyone else waiting to answer who can get in first

[abextra]

Round 384 - He's gone bananas!

The sad answer is that the poor apes won't get any balls from Barry, no matter how many bananas they would bring him.

Let's say Barry gets n bananas. He brings n piles of n crates, i.e. n² crates. He then carries back one crate - so he has n²-1 crates, n balls in each, in total n(n² - 1) balls. In some weird reason - which I hope someone will explain - n(n² - 1) is always divisible by 6 and if Barry paints equal numbers of balls into 6 colours, there will be no white balls left, never.

[davis_greatest]

Round 384 - He's gone bananas!

The sad answer is that the poor apes won't get any balls from Barry, no matter how many bananas they would bring him.

Let's say Barry gets n bananas. He brings n piles of n crates, i.e. n² crates. He then carries back one crate - so he has n²-1 crates, n balls in each, in total n(n² - 1) balls. In some weird reason - which I hope someone will explain - n(n² - 1) is always divisible by 6 and if Barry paints equal numbers of balls into 6 colours, there will be no white balls left, never.

Thank you abextra! And yes, the reason is that n(n² - 1) = (n-1)n(n+1) is the product of 3 consecutive integers, one of which must therefore be divisible by 3 and (at least) one of which must be divisible by 2 - so the product is divisible by 6.

On, then, to...

Round 385 - Up the Wall

Oliver has just got a job helping out in a rather large snooker hall in Great Ape City to help pay his debts after his 15 Valentine’s dinners.

“Listen,” says his new boss, when Oliver arrives at the entrance to the snooker hall, a very long but rather narrow building. “All of my snooker tables run lengthways from east to west, and each table is near either the east wall of my club or the west wall. Some of the tables are ‘east-facing’, by which I mean the baulk cushion is eastwards, and the rest are ‘west-facing’.”

“Right,” nods Oliver.

“Near the east wall,” continues the club-owner, “I’ve got 147 tables, of which half as many are west-facing as are east-facing. Near the west wall, I have more tables – I’m not sure how many, perhaps over 1000 – and all but 147 of those are west-facing.”

“OK,” says Oliver, “so what is my job?”

“What I need you to do, Oliver, is to ensure that the east wall and the west wall both have the same number of east-facing tables! And no playing silly buggers with my club - the tables must, of course, all still be along those two walls and still run lengthways from east to west!”

“No problem!” says strong Oliver, and down he goes to do the job.

However, there is a small problem, which he discovers when he gets down there. The place is so dark that he can’t see a damned thing – he has no way of seeing which tables are facing which way! (And there are no torches, triangles, rests, half-butts, windows or implements of any kind on or around the tables to help him.)

How does Oliver complete his task and pay off his credit card debts?

Answers by Private Message please…

[davis_greatest]

A quick update on round 385 - abextra (yesterday) and now also moglet are the first two to explain how Oliver can achieve his task - congratulations!

The round will remain open for any others trying to help Oliver...

Edit - and Monique too has found the answer - well done!

[davis_greatest]

snookersfun has now joined abextra, moglet and Monique in solving round 385. So, well done to all!

If anyone else wants to try, then we shall leave until 6pm UK time tomorrow. After that time, would someone please put the answer up on the thread.

(... unless there is anyone trying who would like more time, in which case please indicate so beforehand and more time will be allowed )


=================================

Round 386 - Cue Patrol - going bananas :snooker:

(I’m sure this must be a variation of some similar existing puzzle somewhere, but never mind if so!)

Lay 60 cues on the floor. For every square you make, you get one banana.

Now remove whichever cues you like until there are no squares remaining. For each cue you remove, you lose a banana.

Bid here for your bananas (as many as possible). :snooker:

PS When there are any nice bids up, I will ask entrants to demonstrate them with a drawing. I’m not sure I know for sure the maximum possible banana number (or, rather, can prove it to be so, at least as yet – well, I haven’t really considered it...).

[Monique]

Do we need to use all cues?
OK with 60 cues ... 40 bananas

[moglet]

Yes I agree Monique, I thought I had a 41 for this arrangement but alas 40 seems to be the most.