Puzzles with numbers and things

[snookersfun]

have you ever read/seen 'A beautiful mind'? Amazing how much math can slip from your brain...


and, hey, I just turned green- a nice little plus for my headache

[davis_greatest]

No, I've never seen it, but this post is taking me 1/11 of the way to yellow!

[davis_greatest]

Round 14 - A Smack for Luck

I catch up with Damon Grott and we decide to have a friendly game of snooker. These are the rules:

At the end of the frame, we will look at our scores. For every point that I have scored, Grott will write a different odd number (from 1 to 99) on the blackboard. I can then choose any two of the numbers written up and, if I can make them total the exact number of points that Grott scored, I can give him a smack.

Well, I've forgotten my glasses but I break off and leave an easy red on. Grott pots it with a black, then runs out of position and plays safe. I fail to get it safe and leave him on. Again he pots red and black and runs out of position. Still, I don't pot. Next visit, he pots a red and loses position.

This goes on - on each of his next 4 visits he gets red-black each time.

His next visit, he just gets a red. Then he has two more visits, each of red-black, before losing position. His next visit, he pots red-brown and loses position. Then, he pots red-black-red-black, his highest break of the year, and loses position. Still, I can't seem to pot, and let him in. He gets red-pink on the next visit. I leave him on the final red, which he pots with a black before leaving poor position on the yellow. He takes it on, and misses it.

Now, thus far, I still haven't potted a ball (nor has anyone fouled), and all the reds have gone. However, I pot the yellow and clear the colours.

I am delighted, because I know that I am guaranteed to be able to smack Grott. Explain why.

[snookersfun]

so we are still smacking Grott
and of course you can:
Grott got 102 points, you got 27 balls, therefore Grott has to write 27 out of 50 possible uneven #s
in order to reach 102, there are 24 pairs (just 1 and 51 can't be partnered) of uneven numbers leading to that result, you need to find only one such pair, which is guaranteed as Grott has to write 27 numbers (24 each partner + 2 for the two numbers which can't be used, so the 27th number is bound to partner with one of the previous ones).

See, I am getting there after serious editing...

[abextra]

At first you can be delighted, because Grott's score is even, so it is possible to get it by adding two odd numbers. There are 50 odd numbers between 1 and 99 and 24 pairs which gives you the score 102 (3+99, 5+97...). Even if Grott writes numbers 1 and 51, which you don't need at all, he still has to write 25 more and there will be at least one pair of numbers what gives you 102.

ah, late again...

[snookersfun]

abextra, I think we posted the final proof at about the same time, lets share the point, if DG agrees

[abextra]

You were first, snookersfun ,you deserve the point!

[Obligation]

The editing buisness makes it a bit ambiguous though, no?

[davis_greatest]

Dead heat!

Well, with the editing, it is certainly not conclusive who got there first, so, by mutual consent and as we are all friends, we will share the point. No, we won't - I've changed my mind. You both solved it, independently, around the same time... so a whole point each!

That was solved faster than I had thought it would be. Maybe I shall have to pose something harder!

SO HERE IS THE SCOREBOARD AFTER ROUND 14

snookersfun……………………….…..6
robert602…………………………………4
abextra……………………………..…...3½
Vidas……………………………………….1½

(scoreboard adds up to number of rounds+1 since 2 members each got a point for round 14)

[davis_greatest]

Question 15 - The Snooker Plus dozen

This is a slightly more complex variation of a question or two that I set on the Biggest Discussion Ever thread on the BBC site a few months ago. Those who competed then may have an advantage!

Grott is practising his potting with a set of Snooker Plus balls. Snooker Plus was introduced by Joe Davis - similar to snooker, but Davis added an orange ball worth 8 points and a purple ball worth 10 points.

To avoid worrying about position, Grott simply pots balls in any order, one ball at a time - but not worrying about necessarily potting a red before each colour. (Potted colours are immediately respotted.)

Each time he tries this, he always makes a break of 12, before breaking down, and then setting all the balls up and starting again.

He does this many times, and I notice that every single time he makes his 12 break he has potted a different sequence of balls. For example, one time he potted the blue and then the black. Another time, he potted the black and then the blue. Another time, he potted 12 reds in succession. Once, he potted red, purple, red.

My friend and I have been watching him do this many times, when I say to my friend, "I guarantee you that if he makes another 12 break this time, he will repeat one of the sequences we have just seen."

How many times have we watched Grott make a 12 break?

[Obligation]

56?

53?

I'll plump with 53.

[davis_greatest]

56?

53?

I'll plump with 53.

Neither of these! Sorry.

[snookersfun]

2033 now?
(anybody notices this is changing by the minute)

[davis_greatest]

2033 now?
(anybody notices this is changing by the minute)

... is the correct answer! Well done!

SO HERE IS THE SCOREBOARD AFTER ROUND 15

snookersfun……………………….…..7
robert602…………………………………4
abextra……………………………..…...3½
Vidas……………………………………….1½

(scoreboard adds up to number of rounds+1 since 2 members each got a point for round 14)

[davis_greatest]

Next round to follow tonight

I have to do some work now! I will try to post a question on colourful socks tonight.