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# The Impossible 24 Game???

Posted on 2003-11-19
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Today during school I came across a couple of kids trying to figure out one of the cards of "The 24 Game".  This immediately struct me as odd, because being seniors it is very childish to play the game.  If you don't know how it works, the rules are:

1.) Use all numbers once and only once
2.) You can only use the four basic math functions (+ - / *)

So as I was saying, I along with many others spent 20 minutes trying to figure it out and got no where, it has been bothering me all day.  The game is designed for elementary school kids, and I'm in AP Calculus as a sophmore in high school and can't figure it out.  And some of my friends were helping me and they got 1600's on the SAT's and couldn't get it.  So I thought I would post it here and see if any of you could get the answer, or if it is a misprint...I wasn't sure if it was a misprint or not, because the directions of the game say that all have atleast one section.

So here are the numbers:

7
3            3
5

Have fun, don't let it keep you up at night. ;)

Mark
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Question by:simpsons17371
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LVL 31

Expert Comment

ID: 9784906
(75 -3)/3

from understanding brackets are allowed and it can not be done without combing the 7and 5 to make 75 which I also believe is in the rules (I ran a short program to test)
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Expert Comment

ID: 9789420

57-33

meow......
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Accepted Solution

meintsi earned 50 total points
ID: 9789760
Here you go ..................
(following the explicit rules)

((3×5)-7)×3 = 24
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Expert Comment

ID: 9791838
meintsi, ouch! How did my program miss tagt ( and me for that matter)
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Expert Comment

ID: 9791872
hmm, my program did not miss it i did not check the output properly. :-(
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Author Comment

ID: 9792253
thats it, meintsi....i spent so long trying to figure it out and i completely overlooked that, along with a tom of other people.  i wonder what that is all about
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Expert Comment

ID: 9818087
GwynforWeb, would you mind posting the program?

thanks
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LVL 31

Expert Comment

ID: 10048486
Voice,
I just noticed your post. I ran this and then checked through the output for the right number of each number. Save it as a .htm and open in a browser. ( no programing awards here )

<script>
target=24
nums=new Array('3','3','5','7')
ops=new Array('+','-','*','/')
bl='('
br=')'
for (i=0;i<4;i++)
for (j=0;j<4;j++)
for (k=0;k<4;k++)
for (l=0;l<4;l++)
for (o1=0;o1<4;o1++)
for (o2=0;o2<4;o2++)
for (o3=0;o3<4;o3++)
{NumStr=bl+bl+nums[i]+ops[o1]+nums[j]+br+ops[o2]+nums[k]+br+ops[o3]+nums[l]
if (eval(NumStr)==target) document.write(NumStr+'='+target+'<br>')
}
</script>
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