Puzzles with numbers and things

[abextra]

You can split these numbers into three parts - x, y and z. For 153 x=1, y=5, z=3, for 221859 x=22, y=18, z=59, for 828538472 x=828, y=538, z=472 etc. Then

x^3 + y^3 + z^3 = x y z (I'm not sure, how to write it).

For example 153 = 1 + 125 + 27
. . . . . . . . 221859 = 10648 + 5832 + 205379
. . . . . . . . 828538472 = 567663552 + 155720872 + 105154048
etc.

I didn't try every single number, hope it works though.

[davis_greatest]

Congratulations, abextra!

Well done! 1 point! I had wondered whether anyone would ever get that, but a quick answer!

Yes, as examples,

153 = 1^3 + 5^3 + 3^3 (1 cubed + 5 cubed + 3 cubed)

828538472 = 828^3 + 538^3 + 472^3



HERE IS THE SCOREBOARD AFTER ROUND 75, WITH POINTS ADDED FOR SOLUTIONS RECEIVED SO FAR TO ROUNDS 68 & 73 WHICH ARE STILL OPEN

snookersfun……………………….…..35½
abextra...............................19½
davis_greatest.....................15½
Vidas..................................12½
elvaago...............................7
chasmmi..............................6½
robert602.............................6
The Statman……………………...……5
Sarmu..................................4
Semih_Sayginer.....................2½
austrian_girl and her dad.........2½
April Madness........................1

[davis_greatest]

Round 76 - Never a cross word!

I've posted the other crosswords on the sister thread to this, "Puzzles with words and things", but I see no harm in posting one here, given that this thread is called "Puzzles with numbers and things", and words are things, and the clues all have numbers....

So here goes...

Across
1 You'll get this if you strike bottom
8 Play on this baize
9 Don't do this to 8 Across or it will end in tears
10 Applaud this break
11 This Dubliner won UK Championship (2 words)
13 Did he go slowly to Dubai?
16 Get your safety behind this half of 17 Across (2 words)
17 Let's 30 Down from here!
18 Made a skeleton from mixing 13 Across
19 Three for this, so is 8 Across
20 Win this if you want to 30 Down!
21 Worth taking on, it's 12 Down if it doesn't pay off (3 words)
24 Useful for resting 41 Down on! (2 words)
29 Be sure to hit this thin!
32 15 Down carried this air in the '80s
33 Is Williams or Robertson the better one? (2 words)
35 This finish when 6 Down goes 3 Down
36 Challenging pot
38 Romford man wears his crown
39 Get yours in before the tournament!
40 Before 31 Down means 6 Down comes back up!
42 Can this curve result from lifting the 35 Across of the 41 Down?
43 Won a frame against Hendry after losing the first nine, when Hendry won 3rd world title
44 Theatre hosted Grand Prix with 15 Down's world titles' sides

Down
1 Does Alfie have to carry this?
2 Lost 10-6 in Crucible first round to the 15 down, sleeping in his Mondeo? (2 words)
3 Where it is when it enters the pocket
4 This pot from distance can be a 36 Across!
5 Does Ding play this to leave it awkward? (2 words)
6 18.5 million watched 14 Down and the final one well after midnight
7 Playing 15 Down gives you practice in playing from this feather-filled resting place
10 preposition sandwiched in 21 Across
12 No charge for this ball when snookered
14 Does this Irishman come dancing?
15 Is this golden one the greatest ever?
17 This miner used to dig till he won the Masters
18 Willie felt this after missing that easy one
22 his whispers were low
23 Pot a red for this after 28 Down (2 words)
25 Doing this to words in the town with 43 Across
26 Whingeing dynamo champ
27 This commentator wasn't the master from 7 up
28 After the 12th 6 Down when on for the max! (2 words)
30 Get underway (2 words)
31 The 18 Down one is in the centre of 8 Across
34 Sandwiched between Clive and 10 Across for always
37 Is Jimmy good with this X break?
41 No matter how many pieces, must have at least 1 more foot than its wielder!

[chasmmi]

am kind of confused how to fit two words into 17across seeing as the is only one square.

[davis_greatest]

am kind of confused how to fit two words into 17across seeing as the is only one square.

The smart answer would be: write smaller! The real answer is...

"Ooops, sorry - well spotted! I've now corrected this in the post above. 17 Across is not 2 words."

I had also forgotten to say that 5 Down and 28 Down are each two words - also now corrected above! I had a bit of trouble with the "counting to two" thing.

[davis_greatest]

Round 73 deadline has expired!

Oliver, my pet orang utan, has gone to Barry The Baboon's Ball Shop to buy some snooker supplies. Mainly, Barry sells snooker balls, but he sells other things too.

Oliver buys the following (cheapest first, through to the most expensive):

a packet of chalks
an X to go on the end of a rest
a ball marker
a practice cue ball (with markings to see the effect of spin)


Each item is a whole number of pounds and pence. For example £2.50, or £1.14, or whatever. There are 100 pence in one pound.

Before Oliver pays, being a clever fellow, he works out how much the four items will cost. £7.11 is the total.

Barry, at the till, types the prices in (for example, for £2.50 he would type 2.50). However, Barry makes a mistake, and accidentally presses x (multiply) each time, instead of + (plus).

Oliver, when Barry tells him the "total", never spots a thing, and nor does Barry, because the amount that Barry says is £7.11, as Oliver expected!

How much does each item cost?

Answers by Private Message please. Inital Deadline with be 12:00 noon GMT on Sunday 3 December.

The deadline to round 73 has now expired. All points for this have already been awarded, but congratulations again to Sarmu, elvaago and snookersfun who correctly found that the items cost £1.20, £1.25, £1.50 and £3.16.

We find that
1.20 + 1.25 + 1.50 + 3.16 = 7.11
and
1.20 x 1.25 x 1.50 x 3.16 = 7.11

As a start, if the prices in pence are A, B, C, D
we have
A + B + C + D = 711
A.B.C.D = 711000000

You can find that the factorisation of 711000000 is
711 x 10^6
= 9 x 79 x 2^6 x 5^6

so the prime factorisation is

2^6 x 3^2 x 5^6 x 79.

So one of the prices is divisible by 79p - a little more work shows that this one is 316p.

Then you can find that another one must be divisible by 5^3 - that one turns out to be 125p (you need to try a few possibilities to find this).

Once you have found two of the prices, the problem turns into two equations with two unknowns... and (by solving a quadratic equation) the problem is solved!

[davis_greatest]

Round 76 update!

Ooops - there was an error in the original grid in that number 41 appeared twice! I've now corrected this in the grid above - this has also changed the numbering of the last three across clues. There is now only one 41!

[chasmmi]

I have a question but have no idea what number it is (shows what use I am in this thread.)

After shooting Oliver the orangutan for irritating him little Jimmy had a thought. Thinking back to a previous question about number of digits from one to one hundred million he decided to work out his own problem. he wondered how many letters there are from one to ten million.

This means one is 3 letters, two is 3 letters, three is five letters so there are 11 lettters from one to three.

So how many letters are there from one to ten million?

To make this interesting I am going to award myself 5 points. For every person who gives me the correct answer they will get one of my points. If six people give me the right answer I will begin to lose one of the 6.5 points i had before so i could lose or gain a lot here.

Therefore obviously answers by PM PLEASE.

(if this above idea is not liked I will scrap it).

[davis_greatest]

I will propose a change to the scoring, chasmmi - if no one gets it, you may have one point. And, however many people get it, you will not be deducted any points...

We need a convention for naming numbers and when to use "AND" ... I suggest for the purpose of this question that 7,321,419 would be written

SEVEN MILLION THREE HUNDRED AND TWENTY ONE THOUSAND, FOUR HUNDRED AND NINETEEN.

[davis_greatest]

Actually, this will get confusing. For example, is 7,019,000
SEVEN MILLION AND NINETEEN THOUSAND
or
SEVEN MILLION NINETEEN THOUSAND?

and how about 7,000,002 ?

chasmmi, shall we do this ignoring "AND"s for the purpose of this question?

[chasmmi]

in this situation 'and' always follows hundred, the only other occasion is when the unit is less than one hundred as in 1005 or 1,000,023.

7,019,000 is seventeen million, nineteen thousand. then seventeen million nineteen thousand and one...

[davis_greatest]

in this situation 'and' always follows hundred, the only other occasion is when the unit is less than one hundred as in 1005 or 1,000,023.

7,019,000 is seventeen million, nineteen thousand. then seventeen million nineteen thousand and one...

hopefully seven million, not seventeen...

How would we write 7,106,020? Do we use two "AND"s:

SEVEN MILLION ONE HUNDRED AND SIX THOUSAND AND TWENTY

[chasmmi]

yes but in this number scale two is the maximum there can be. no number will have three ands between one and ten million.

[davis_greatest]

Snookersfun has solved the crossword!

SO HERE IS THE SCOREBOARD AFTER ROUND 76, WITH POINTS ADDED FOR SOLUTIONS RECEIVED SO FAR TO ROUND 68, WHICH IS STILL OPEN BUT ONLY FOR A SHORT WHILE LONGER

snookersfun……………………….…..36½
abextra...............................19½
davis_greatest.....................15½
Vidas..................................12½
elvaago...............................7
chasmmi..............................6½
robert602.............................6
The Statman……………………...……5
Sarmu..................................4
Semih_Sayginer.....................2½
austrian_girl and her dad.........2½
April Madness........................1

[davis_greatest]

I've just found this and reminded myself what the deadline is. There are 40 minutes to go for anyone wishing to join Sarmu, snookersfun, abextra, chassmi and austrian_girl in scoring points for this round...

Would you like another Ape Break round?

I'm sure you are familiar with the rules by now. You need to find the highest break you can (without using a free ball).

This time, it's a bit different. It's like normal snooker, still with 15 reds, but now there are 4 extra colours. You have to pot red, colour, red, colour etc, just like in normal snooker, but then pot the 10 colours in order (instead of the usual six).

The colours are:

yellow: 2 points (if you can't read that, it says yellow: 2 points)
green: 3 points
brown: 4 points
blue: 5 points
pink: 6 points
black: 7 points
orange: 8 points
silver: 9 points
olive: 10 points
purple: 11 points


There are now 10 pockets (one extra pocket added on each edge of the table). From top left, going clockwise, the pockets are:

purple, brown, orange, green, pink, silver, blue, olive, yellow, black

So the table looks a bit like this - I've put the value of the colour of each pocket to help you see, in case you are colour blind.

11-------4-------8
!......................!
!......................!
!......................!
7.....................3
!......................!
!......................!
!......................!
2.....................6
!......................!
!......................!
!......................!
10-------5-------9


The rules are

a) Once a colour has been potted, the same colour cannot be potted following the next red, nor following the red after that. (Once the 15th red and colour have been potted, this rule no longer applies - the final colours may and must be potted in the usual order of yellow, green, brown, blue, pink, black, orange, silver, olive, purple, regardless of the colours potted with the final reds.)

Example 1: Red Brown Red Yellow Red Blue Red Brown IS allowed
BUT
Example 2: Red Brown Red Yellow Red Brown IS NOT

Example 3: For the 14th and 15th reds,
Red Black Red Yellow Yellow Green Brown Blue Pink Black Orange Silver Olive Purple IS allowed


b) Whenever a colour has been potted into a corner pocket, the following colour cannot be potted into any pocket that lies along the same edge - that means it may not be on the same side (left or right) of the table, nor at the same end (top or bottom).

Example A: after potting a colour into the orange pocket, it would not be permissible to pot the next colour into the orange, green, pink or silver pockets (same side), nor into the purple or brown pockets (same end).

c) Whenever a colour has been potted into a pocket that is not a corner pocket, the following colour must be potted into a corner pocket, but must not lie on the same edge.

Example B: after potting a colour into the yellow pocket, the following colour can only be potted into the orange or silver pockets.

Example C: after potting a colour into the blue pocket, the following colour can only be potted into the orange or purple pockets.

d) Rules b) and c) apply even when down to the final 10 colours after all the reds have gone.

e) None of these rules apply to reds. It makes no difference into which pockets reds are potted.

f) And this is the important bit: potting a colour into a pocket of the same colour as the ball (e.g. pink into pink pocket) scores double points (in this example 2 x 6 = 12).


As ever, your question is: what is the highest break (ignoring free balls) you can make?

You don't need to say the highest theoretically possible - you just need to send me the highest break that YOU can find by Private Message by the Initial Deadline of 18:00 GMT on Sunday 3 December.


If you have any questions, please ask them on the thread.


You should explain how you get your break. For example, you might say:

Red
Green into Yellow pocket (or whatever)
Red
Pink into Orange pocket (or whatever)
....
...

and after all 15 reds and colours...

Yellow into Yellow pocket (or whatever)
Green into Silver pocket (or whatever)
Brown into Black pocket (or whatever)
....