Puzzles with numbers and things

[PaulTheSoave]

Unfortunately, cause lack of time, I can just read some posts and post the occasional message nowadays.

[snookersfun]

Hi Paul, there are worse off-topics than this...
considering that most riddles were about snooker here...

[davis_greatest]

Question 23 - Guess the girls' ages

Although question 22 is still open, I'll set question 23 now before I go away for a few days. This one is intended to take a little longer to solve - but it's always hard to tell!

-----------------------------------------------------------------

Oliver, whom you will know very well by now as my pet orang-utan, goes on holiday to Krypton to watch a snooker tournament, which never stops. They play snooker there every day, just like snooker on Earth, except there is no "free ball" rule (so the maximum break is 147). Oliver arrives to see the first day's play, and stays there each day after that.

Every day, they flash up on a big screen the top century break that was made that day (if one was). Every time that the top century break is different from all the top century breaks that have come before, everyone in the audience is given a golden ball to keep as a souvenir.

Eventually, realising he will get no more golden balls, Oliver comes home.

Part a (easy) - how many golden balls does Oliver bring home?

-----------------------------------------------------------------

Then Gordon, whom you will also know very well by now as my pet gorilla, goes on holiday to Moominon to watch a snooker tournament, which never stops. He arrives at the start of the month in time for the start of the tournament.

On Moominon, they play snooker just like on Krypton, with no free ball, except that on Moominon the players are very good and every time that a player wins a frame, he always makes a break at least as high as the highest break made in the Final by the winner of the 2006 888.com World Snooker Championship (which I will be nice and tell you was 68).

Every day, the officials write up on a blackboard, in descending order, the top 5 breaks made that day. (More than 5 frames are played a day, so they can always find a top 5, each one at least 68.) For instance, they might write "134, 126, 103, 103, 76". (If there are two or more "5th-equal" breaks - so if there were more than one 76 break in this example - they would only write one of them, so the list would still appear as shown above.)

At the end of each month (which happens to consist of 1 million very quick days on Moominon), everyone in the audience is given a transparent goody bag. Oliver eats the goodies but keeps the bags as souvenirs.

Gordon likes to keep track of these daily lists of the top 5 breaks. It's incredible, but every day Gordon notices that the list is different from every previous day - i.e. never the same list twice! This goes on, until one day Gordon realises that if he stays another day, a list is bound to come up that will be the same as one of the ones he has seen before. So he comes home with his empty goody bags.

Part b (harder) How many empty goody bags does Gordon bring home?

-----------------------------------------------------------------

When they get home, Charlie, whom you will also know very well by now as my pet chimpanzee, lays out all of Gordon's empty goody bags in a long straight line on the floor. Into each, he puts at least one golden ball, until all of Oliver's golden balls are in bags.

(If you have more bags than balls, you need to go back and check your parts a and b.)

Then, Florence, Elizabeth, Sylvia and Talia (all of whom are aged younger than the number of goody bags) come to visit. Charlie tells them that if any girl can find a set of one or more adjacent bags, containing a total number of balls equal to her age, then she can keep those bags and the balls they contain. For example, if a girl is 10, and if there are 7 balls in bag 4, 1 ball in bag 5 and 2 balls in bag 6, she could take those 3 bags as the number of balls adds up to her age (10) and the bags are adjacent. In this example, if she were aged 7, she could simply take bag 4.

Any balls not taken will be kept by clever Charlie. He doesn't know the girls' ages but wants to keep as many balls for himself as he can.

Florence, the youngest, steps up, but sadly cannot find any bags that work, and goes home empty-handed. Then up steps Elizabeth, the next youngest. She leaves and goes home, just as disappointed. Then up comes Sylvia, older still, and she has no more success, so also goes home.

Finally, Talia, a year older than Sylvia, picks a bag and goes home with her balls.


Part (c) (not sure how hard you will find this):
How old is each girl, and how many golden balls does Charlie keep?


* "older" means at least one year older

[davis_greatest]

Oh - and there will be somewhere between 2 and 3 points available for question 23, depending on the elegance of the solution and on which parts are solved.

[davis_greatest]

Question 24 - WT finishes with lots of round numberrs

Remember that questions 22 and 23 are still in progress! But I'll add to it question 24. A nice easy one!

Willie Thorne is practising at home. He first thinks of a number. The number he thinks of is 147. He counts each ball that he pots and each time he multiplies the number he had by the number of that ball, keeping a running product.

For example, when he pots the first ball (a red), he multiplies 147 by 1 and gets 147. He then pots his second ball (a black) and multiplies that 147 by 2 to get 294. He then pots his third ball (a red) and multiplies the 294 by 3 to get 882. Then when he pots the next black (his 4th ball), he gets 882 x 4 = 3528. And so he continues...

During the session, he makes 147 maximum breaks, i.e. 147 breaks of 147. (Each time that he starts a new frame, he continues counting - he does NOT start back at 1.)

With how many zeroes does the rather large number that he ends up with finish?

(For example, 37 million = 37,000,000 finishes with 6 zeroes. So if he finishes with 37 million, your answer would be 6.)

[davis_greatest]

Question 25 - WT tiles his bathroom floor!

Remember that questions 22, 23 and 24 are still in progress! Here's question 25 in case they get done quickly!

This time, it is WT who is tiling his bathroom floor! It's 147 inches wide and 147 inches long - a perfect square with no sink, toilet, bath or shower to worry about. He has some tiles (which he cannot cut) which come in 147 different colours. He wants to use as many different colours as possible. The tiles are all pretty small - some have area of 4 square inches and some have area 3 square inches. Tiles may not overlap and he must cover the whole floor.

They come in these shapes (it's not very easy to draw these, but they consist of one-inch squares where I show "0" - they have straight edges, not round, but hopefully you get the idea):

The ones with area of 4 square inches:

OO
OO


and

..OO
OO

and

OO
..OO


The ones with area of 3 square inches:

O
OO

which can also be rotated.


Show that, in order to tile his floor, WT must use at least 3 of the tiles of 3 square inches of the same colour.

[April madness]

Answer to Q24 - 31?

Oh forget it, that wasn't even a good try.

[davis_greatest]

Answer to Q24 - 31?

Oh forget it, that wasn't even a good try.

More than that April. Remember that he makes 147 breaks of 147.

[April madness]

Yeah, I know - I didn't read the question properly that he continues to count rather than starts from 1 again

but now I know why he's bald - too many zeros to keep in his head

[snookersfun]

excell is not very helpful again....

[snookersfun]

Re. 24:
is 5297 anywhere in the neighborhood?

[davis_greatest]

Re. 24:
is 5297 anywhere in the neighborhood?

Not really!

[snookersfun]

sorry, just got to that conclusion myself

[snookersfun]

Question 24 still
is 17411 any better?

[snookersfun]

Question 24 still
is 17411 any better?

counting 0 s though (I'm still a bit condused by the question), that should rather be: 17400