Puzzles with numbers and things

[snookersfun]

Hi dg, got involved into Potblack instead.
don't really know, what to make out of this question here... sorry

[davis_greatest]

Hi snookersfun. Does the question make sense to you now? Are you struggling with the question, or just the answer?!

[snookersfun]

OK, yes, but explanation???

15 games, pairings can be arranged in groups of 5,4,3,2,1 (according to slap/pot as well) . Now for each scenario of 1-15 games with same results, you can find a group of three players, can't you?

Help

[snookersfun]

Part b) is asking you to prove that, after all possible pairings have been together, you can find a group of at least 3 players (such as, Hiffiths, Griggins and Rawburn, say) such that they had either ALL smacked each other or ALL given each other pots of jam.

still sorry ignore that, just caught my hang-up, of course there are only 6 players!!! Give me a sec...

[davis_greatest]

Would have thought 3h45 min (player 1 with 2,3,4,5,6 each; 2 with 3,4,5,6; 3 with 4,5,6; 4 with 5,6; 5 with 6)

You can do it faster than 3 hours and 45 minutes!

[davis_greatest]

First, they get together in pairs - all possible pairings being formed. They both give and receive while in pairs. So if, say, a particular pair is Hiffiths and Griggins, then either
(i) Hiffiths smacks Griggins and Griggins smacks Hiffiths; or
(ii) Hiffiths gives Griggins some pots of strawberry jam and Griggins gives Hiffiths some pots of strawberry jam.

Part b) is asking you to prove that, after all possible pairings have been together, you can find a group of at least 3 players (such as Hiffiths, Griggins and Rawburn, say) such that they had either ALL smacked each other or ALL given each other pots of jam.

[snookersfun]

Sorry, you lost me on this one: isn't the 'group' thing contradicting the 'alone' statement?
And also does only one of the players in each couple act, while the other receives?

Each player spends 15 minutes alone with each other player (so during this time, each possible pair spends 15 minutes together).

a) What is the minimum period of time that this game must last, for all pairs to spend time together? Show how the pairings can go to achieve this time.
Would have thought 3h45 min (player 1 with 2,3,4,5,6 each; 2 with 3,4,5,6; 3 with 4,5,6; 4 with 5,6; 5 with 6)
b) Show that there must be at least one group of at least 3 players, such that either
- all of them have given all the other players in that group pots of strawberry jam, or
- all of them have given all the other players in that group smacks to the face.

[davis_greatest]

Pot Smack - The Morning After

Rumour has it that Grott might be Scottish, but more than that I do not know. No one could understand what he said, so not too much is known about him. As for Maun Shirty, I have no idea.

Thank you - good to hear you liked the questions! I don't teach maths, but hopefully can still remember a little.

Yes, of course I make the questions up.... except this next one, which is a standard problem:

Question 10: Pot Smack - The Morning After

The morning after the Pot Smack tournament (of question 9), all the players other than Grott and Shirty get together for some more Pot Smack celebratory action. Each player spends 15 minutes alone with each other player (so during this time, each possible pair spends 15 minutes together - remember that Grott and Shirty play no part in any of this).
[Edit following snookersfun's question below: by "alone", I mean the two players in the pair are alone TOGETHER, i.e. just the two of them, at a time.]

During the 15 minutes, each pair plays either Pot or Smack. Playing Pot involves each player giving his partner pots of strawberry jam. Playing Smack involves each player smacking his partner's face repeatedly.

Questions:

a) What is the minimum period of time that this game must last, for all pairs to spend time together? Show how the pairings can go to achieve this time.

b) Show that there must be at least one group of at least 3 players, such that either
- all of them have given all the other players in that group pots of strawberry jam, or
- all of them have given all the other players in that group smacks to the face.

[snookersfun]

By the way, do we know, who of the two is Shirty and who is Grott?

to screen

great fun your questions.
Are you in math (teacher or study?)
Are you making these things up by yourself?
How are you doing in IQ tests? You have to be a genius

[davis_greatest]

I am also in discussions with BBC and sponsors to see if we can get this Pot Smack televised. Do you think there will be interest?

Shall think up next question soon....

[davis_greatest]

Perfect answer!

Well done, snookersfun! A perfect answer, and very well explained. (Probably the reason you did not see that earlier was that I had forgotten to mention it and only noticed after you had read the question!)

Shirty indeed reached the final but, suffering from a number of well-placed smacks in the earlier rounds, was then comfortably beaten by the number 1 seed!

As you say, the only combination of Shirty's and Grott's seedings for which the total smacks falls between 147 (i.e. 7x21 pots) and 252 (i.e. 7x36 pots) is 2 and 7.

[snookersfun]

Excellent snookersfun! I had originally omitted (and added, I think after you had already read the question) that: "The tournament winner's face was unsmacked throughout the tournament, but he was given a special smack when he collected the trophy."

Can you therefore complete the answer using this information?

Didn't see that at all, that makes it easier: if the winner wasn't smacked + higher seeded than 2 (who got his fair # of slaps and had to reach the finals, he has to be the #1 seed.

[davis_greatest]

Excellent, snookersfun! I noticed that I had originally omitted (and added, I think after you had already read the question - apologies) to mention that: "The tournament winner's face was unsmacked throughout the tournament, but he was given a special smack when he collected the trophy."

Can you therefore complete the answer using this information?

[snookersfun]

OK, I'll try (in no way complete, I am sure)
i) What are Shirty's and Grott's seedings? 2 and 7

ii) State whether it is possible, from the information given, to determine the seedings of the winner and the runner-up of the tournament.
One of them is seeded 2nd. I don't think one can determine the other seeding, except that it wasn't the 7th seed

iii) If it is possible, what the seedings of the winner and the runner-up of the tournament? possibly 1st and 2nd

Explanations:
There are 7 games in your smack game, meaning max. 252 smacks all over (reds w. colours) or min 147 smacks. Also each of the two should be slapped a min. of 21+ times as there are at least 2 games in the first round, where they don't participate. Checking out the possible permutations of S^G+ G^S, one is only left with 2^7 = 128 slaps for the looser (7th seeded player) + 7^2 = 49 for the 2nd seeded player (=177 slaps allover)
In order for that to happen (difference of 79 smacks) the 2nd seeded player has to reach the final, while the 7th seed goes out in the first round (as all others distribute equally). As far as I see, he doesn't have to win though. Now if he looses (have to work out why that has to be so)than of course the winner is the 1st seed!

[Semih_Sayginer]

bugger the questions. i just want to see this in reality.