Puzzles with numbers and things

[abextra]

I started with small numbers of balls and found out, that most of times the player who starts the rolling, can win the game. The second player can win only every fourth game, when there are 4n+1 balls on the table (n= 1, 2, 3, ... ). It means, if Gordon starts the match, he wins the first two games with 15 and 16 balls on the table, then Charlie wins the games with 17, 18, 19 and 20 balls, the next four games will be won by Gordon etc. Gordon will be the first to win 10 games, when Charlie has won only 8, but the difference between them won't be more than 2 wins, no matter how long they will play.

Sorry for my English.

[davis_greatest]

That's right - well explained. Gordon wins the first 2 games. Then Oliver wins 4, then Gordon wins 4, Oliver wins 4... etc, until Gordon reaches 10 with the score 10-8.

Each time an ape can take one, two or three balls. The first ape should try to ensure that the number of balls remaining for the second ape will be 1 more than a multiple of 4, i.e. should try to leave 1, 5, 9, 13, 17, 21, etc

Then, however many balls the 2nd ape takes each time, the first ape should always leave again 1 more than a multiple of 4 - he can do this by taking 4 minus the number of balls just taken (so if 1 was taken, he takes 3; if 2 were taken, he takes 2; if 3 were taken, he takes 1).

Therefore, the starting ape will always win the game unless the number of balls to start with is 1 more than a multiple of 4, which happens every 4th game.


Game 1: 15 balls to start. Gordon takes 2 in his first turn, to leave 13. However many Oliver then takes, Gordon leaves 9. Then Gordon leaves 5. Then leaves 1 - Gordon wins

Game 2: 16 balls to start. Gordon takes 3 in his first turn, to leave 13 - Gordon wins as before

Game 3: 17 balls to start. However many Gordon takes, Oliver can make sure that he leaves 13 for Gordon. -> Oliver wins and starts the next game

Game 4: 18 balls to start. Oliver takes 1 ball to leave 17. -> Oliver wins

etc


Game 1: 15 balls to start. Gordon wins.
Game 2: 16 balls to start. Gordon wins.
Game 3: 17 balls to start. Oliver wins.
Game 4: 18 balls to start. Oliver wins.
Game 5: 19 balls to start. Oliver wins.
Game 6: 20 balls to start. Oliver wins.
Game 7: 21 balls to start. Gordon wins.
Game 8: 22 balls to start. Gordon wins.
Game 9: 23 balls to start. Gordon wins.
Game 10: 24 balls to start. Gordon wins.
Game 11: 25 balls to start. Oliver wins.
Game 12: 26 balls to start. Oliver wins.
Game 13: 27 balls to start. Oliver wins.
Game 14: 28 balls to start. Oliver wins.
Game 15: 29 balls to start. Gordon wins.
Game 16: 30 balls to start. Gordon wins.
Game 17: 31 balls to start. Gordon wins.
Game 18: 32 balls to start. Gordon wins.


So Gordon wins 10-8

[davis_greatest]

....then Charlie wins the games with 17, 18, 19 and 20 ....

Except Charlie isn't playing! It's Gordon and Oliver.

[abextra]

Sorry!

[snookersfun]

whoohee, 3/10 on my way to a banana

[davis_greatest]

Round 63 and round 64 update

With abextra now having submitted the maximum breaks possible to both Bigger Ape Break and Smaller Ape Break a few minutes ago, she has now secured 2 points for each of these two rounds, thus jumping a meteoric 4 points in a matter of minutes...


SO HERE IS THE SCOREBOARD AFTER ROUND 65, BUT BEFORE THE CONCLUSION OF ROUNDS 63 AND 64 (with snookersfun’s, chasmmi’s and abextra's points scored so far on these rounds already included)

snookersfun……………………….…..30
abextra……………………………..…...16
Vidas……………………………………….12½
davis_greatest…………………..……12½
robert602…………………………………6
elvaago...............................5
The Statman……………………..……3
chasmmi ………………………………….3
Semih_Sayginer.....................2½

(some rounds may be worth more than one point)
(especially ones won by davis_greatest)

[snookersfun]

well done Abextra!

[abextra]

well done Abextra!

Thank you, snookersfun! 16% of a banana!

[abextra]

Except Charlie isn't playing! It's Gordon and Oliver.

The phaonmneel pweor of the hmuan mnid.

I cdnuolt blveiee taht I cluod aulaclty uesdnatnrd waht I was radneig. Aoccdrnig to a rscheearcr at Cmagbride Uinervtisy, it deosn't mttaer in waht oredr the ltteers of a wrod are, the olny iprmoatnt tihng is taht the frist and lsat ltteer be in the rghit pclae.The rset can be a taotl mses and you can sitll raed it wouthit a porbelm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe. Amzanig, huh?

Isn't it funny, that I can easily understand this text and at the same time I'm not able to see difference between names Oliver and Charlie?

[snookersfun]

The phaonmneel pweor of the hmuan mnid.

I cdnuolt blveiee taht I cluod aulaclty uesdnatnrd waht I was radneig. Aoccdrnig to a rscheearcr at Cmagbride Uinervtisy, it deosn't mttaer in waht oredr the ltteers of a wrod are, the olny iprmoatnt tihng is taht the frist and lsat ltteer be in the rghit pclae.The rset can be a taotl mses and you can sitll raed it wouthit a porbelm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe. Amzanig, huh?

Isn't it funny, that I can easily understand this text and at the same time I'm not able to see difference between names Oliver and Charlie?

lol abextra! That has to be a girl's thing again. (Phew, at least it is not Alzheimers) I am always, but always, mixing up these names. Could read your text easily as well. We would now need some feedback from male subjects on this.

[Snooker Rocks!]

Looks fine to me

[snookersfun]

an easy one for in between...

Suppose you had a bag with 600 red snooker balls and would at each turn randomly take 15 of them and mark them. At the best case scenario (choosing only unmarked balls) it is clear that one could mark all balls after 40 turns. But picking the balls randomly (or blind) how many balls would be probably marked after 40 turns and how many turns would one need to mark 90% of the balls.
Excel solutions worth 1/2 point, others 1 point. (by PM)
Deadline Tuesday-12:00 pm (GMT)

Everybody hold his/her horses, we are rewording!

[davis_greatest]

Gordon, Charlie and Oliver all understood it perfectly too.

I couldn't understand a word.

Edit: this was referring to the post with letters mixed up - not to snookersfun's question which appeared at the same time.

[davis_greatest]

Scoreboard after round 65

With the deadlines for Bigger Ape Break and Smaller Ape Break expired, below is the confirmed scoreboard.

snookersfun and abextra are invited to post their solutions showing how a break of 199 can be achieved in Bigger Ape Break - this is the maximum possible.

snookersfun, chasmmi and abextra are invited to post their solutions showing how a break of 154 can be achieved in Smaller Ape Break - again, the maximum possible.



HERE IS THE SCOREBOARD AFTER ROUND 65

snookersfun……………………….…..30
abextra……………………………..…...16
Vidas……………………………………….12½
davis_greatest…………………..……12½
robert602…………………………………6
elvaago...............................5
The Statman……………………..……3
chasmmi ………………………………….3
Semih_Sayginer.....................2½

(some rounds may be worth more than one point)
(especially ones won by davis_greatest)

[davis_greatest]

an easy one for in between...

Suppose you had a bag with 600 red snooker balls and would at each turn randomly take 15 of them and mark them. At the best case scenario (choosing only unmarked balls) one could mark all balls after 40 turns, but how many balls would be actually marked after those 40 turns and how many turns would one need to mark 90% of the balls.
Excel solutions worth 1/2 point, others 1 point. (by PM)
Deadline Tuesday-12:00 pm (GMT)

This, of course, is round 66.