Puzzles with numbers and things

[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

[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]

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]

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]

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?

[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.

[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]

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!

[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]

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.

[chasmmi]

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

[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!

[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

[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]

Round 75 - Split the cube

Here is an interesting list of numbers. They all have something in common – and are the smallest numbers that have this property. What is it?

153, 370, 371, 407, 165033, 221859, 336700, 336701, 340067, 341067, 407000, 407001, 444664, 487215, 982827, 983221, 166500333, 296584415, 333667000, 333667001, 334000667, 710656413, 828538472

Answers may be posted on this thread.