24 challenge (new developments!)

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24 challenge (new developments!)

Postby udosuk » Wed Aug 02, 2006 6:20 pm

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*4
5,6,7,8: 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.
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Re: 24 challenge

Postby JPF » Wed Aug 02, 2006 9:29 pm

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 )

:DJPF
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Re: 24 challenge

Postby udosuk » Wed Aug 02, 2006 10:04 pm

JPF wrote:I try :

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

... in base 8 ( octal )

:D

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

No, that's not right... The system stays in base-10... (Sorry for not specifying it initially...)
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Re: 24 challenge

Postby underquark » Wed Aug 02, 2006 10:26 pm

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.
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Postby udosuk » Wed Aug 02, 2006 11:55 pm

Great job underquark!:D

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)...

:idea:
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Postby udosuk » Thu Aug 03, 2006 1:34 am

Forget about those extra points... Just do some more...
Code: Select all
1,1,6,9
1,2,7,7
1,4,5,6
1,6,7,9
2,4,5,5
2,4,7,7
2,5,7,8
2,7,8,9

Some of them are definitely easier than others...
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24 challenge

Postby Cec » Thu Aug 03, 2006 6:51 am

udosuk wrote:Great job underquark!:D
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?:)

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Postby udosuk » Thu Aug 03, 2006 9:31 am

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
1,6,6,8
2,5,7,9
3,3,7,7
4,4,7,7
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Postby JPF » Thu Aug 03, 2006 10:29 am

Code: Select all
1,1,6,9 : 24=(1+1)*9+6
1,2,7,7 : 24=((7*7)-1)/2
1,4,5,6 : 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)*2-4
2,5,7,8 : 24=(5*2-7)*8
2,7,8,9 : 24=2*(9+7)-8
1,6,6,8 : 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 ?:D
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24 challenge

Postby Cec » Thu Aug 03, 2006 10:43 am

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.:)

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Postby udosuk » Thu Aug 03, 2006 11:47 am

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...:D

Word is that JPF is a very good programmer:) (I'm not implying anything...:D )
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24 challenge

Postby Cec » Thu Aug 03, 2006 2:04 pm

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

I was wondering how JPF was so quick and me so slow.. anyway at least I scored a point.
:)
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Postby JPF » Thu Aug 03, 2006 4:00 pm

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
1,1,1,8
1,1,8,8
1,5,5,5
2,2,3,5

etc...

I have a long list if you need more.

Can I get my 900 points (3600 ?) please:)

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Postby udosuk » Thu Aug 03, 2006 4:03 pm

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.
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Postby udosuk » Thu Aug 03, 2006 4:10 pm

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?
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