## 24 challenge (new developments!)

Anything goes, but keep it seemly...

### 24 challenge (new developments!)

Anyone has played the game 24 challenge?

Your're given 4 single digit numbers... You can only apply 4 operations on them: addition/subtraction/multiplication/division... You can use as many brackets as you like... All digits must be used once and only once... You cannot combined digits together to form larger numbers (e.g. 1 and 2 must be treated separately and not as 12 or 21 together)... Nor could you express any decimal number using "."...

Examples:
Code: Select all
`1,2,3,4: 24=1*2*3*45,6,7,8: 24=(7+5)*(8-6)0,3,6,8: 24=8*3+(6*0)1,9,8,6: 24=1*(9-6)*8`

Could anyone work out how to do this for:
1,3,4,6
Last edited by udosuk on Mon Aug 21, 2006 6:28 am, edited 1 time in total.
udosuk

Posts: 2698
Joined: 17 July 2005

### Re: 24 challenge

udosuk wrote:Could anyone work out how to do this for:
1,3,4,6

I try :

6*4 - (3+1) = 30 - 4 = 24

... in base 8 ( octal )

JPF
JPF
2017 Supporter

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Location: Paris, France

### Re: 24 challenge

JPF wrote:I try :

6*4 - (3+1) = 30 - 4 = 24

... in base 8 ( octal )

Now, that's what I call stealing base...

No, that's not right... The system stays in base-10... (Sorry for not specifying it initially...)
udosuk

Posts: 2698
Joined: 17 July 2005

### Re: 24 challenge

udosuk wrote:Could anyone work out how to do this for:
1,3,4,6

Yep! I'm pretty sure there is a list of all solutions out there somewhere anyway.
Teensy writer wrote:6/(1-3/4); 1-3/4 is 1/4 and 6 divided by this is the same as 6x4 = 24.
Last edited by underquark on Thu Aug 03, 2006 6:35 pm, edited 1 time in total.
underquark

Posts: 299
Joined: 06 September 2005

Great job underquark!

You score 49 points... 1 more point will be awarded if you fix the typo error within your attempted answer...

50 more points will be awarded if you can prove that the answer is unique...

900 more points will be awarded if you can find another set of 4 single digit numbers with a unique answer (or prove no such set exists)...

udosuk

Posts: 2698
Joined: 17 July 2005

Forget about those extra points... Just do some more...
Code: Select all
`1,1,6,91,2,7,71,4,5,61,6,7,92,4,5,52,4,7,72,5,7,82,7,8,9`

Some of them are definitely easier than others...
udosuk

Posts: 2698
Joined: 17 July 2005

### 24 challenge

udosuk wrote:Great job underquark!
You score 49 points... 1 more point will be awarded if you fix the typo error within your attempted answer..."

udosuk wrote:Your're given 4 single digit numbers... You can only apply 4 operations on them:

Do I earn a bonus point now or when I submit an answer?

Cec
Cec

Posts: 1039
Joined: 16 June 2005

Well done Cec, 1 bonus point for spotting my typo...

Why not try earning 50 points by solving one of the challenges? Some of them are really easy...

Some more (tougher) ones:
Code: Select all
`1,6,6,82,5,7,93,3,7,74,4,7,7`
udosuk

Posts: 2698
Joined: 17 July 2005

Code: Select all
`1,1,6,9 : 24=(1+1)*9+61,2,7,7 : 24=((7*7)-1)/21,4,5,6 : 24=6/(5/4-1)1,6,7,9 : 24=(1+7)*(9-6)2,4,5,5 : 24=4+2*(5+5)2,4,7,7 : 24=(7+7)*2-42,5,7,8 : 24=(5*2-7)*82,7,8,9 : 24=2*(9+7)-81,6,6,8 : 24=6/(1-6/8) 2,5,7,9 : 24=(7*5)-(9+2)3,3,7,7 : 24=7*(3+3/7)4,4,7,7 : 24=7*(4-4/7)`

How many points ?
JPF
JPF
2017 Supporter

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Joined: 06 December 2005
Location: Paris, France

### 24 challenge

2 , 5 , 7 , 8...

24 = (2*5 - 7) * 8

If this is correct am I now 50 points or 51 points.? I did spot the typo first OK .. I'll settle for 50 points.

Cec
Cec

Posts: 1039
Joined: 16 June 2005

Sorry Cec, JPF likes to play monopoly and has grabbed all 600 points... He beat you by just about 15 minutes...

You're still on 1 point for now... Perhaps you could pick up some more typos here for a few more...

Word is that JPF is a very good programmer (I'm not implying anything... )
udosuk

Posts: 2698
Joined: 17 July 2005

### 24 challenge

udosuk wrote:"...Word is that JPF is a very good programmer (I'm not implying anything... )"

I was wondering how JPF was so quick and me so slow.. anyway at least I scored a point.

Cec
Cec

Posts: 1039
Joined: 16 June 2005

udosuk wrote:900 more points will be awarded if you can find another set of 4 single digit numbers with a unique answer (or prove no such set exists)...

Here are some :
Code: Select all
`1,1,1,81,1,8,81,5,5,52,2,3,5`

etc...

I have a long list if you need more.

Can I get my 900 points (3600 ?) please

JPF
JPF
2017 Supporter

Posts: 3755
Joined: 06 December 2005
Location: Paris, France

JPF, in case you're really using a program, it'd be good fun to discuss about it too...

I myself wrote a BASIC program to do it (yes I'm from the ancient school)... It could search all 715 different combinations of 4 single-digit numbers (duplicate or not) for all possible formulas...

I'd also like to find out which of them have unique solutions, but my program couldn't do it efficiently... Any ideas?

[Edit: Wrong statistical data deleted... ]
Last edited by udosuk on Fri Aug 04, 2006 3:27 am, edited 1 time in total.
udosuk

Posts: 2698
Joined: 17 July 2005

JPF wrote:I have a long list if you need more.

Can I get my 900 points (3600 ?) please

Those 900 points are for the collective effort of finding extra sets with unique solutions (you should notice I've found some more myself too)... But you earned them... So you tally is 1500 now, big roller...

Do you have a comprehensive list? And how could you be sure?
udosuk

Posts: 2698
Joined: 17 July 2005

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