code:

---

a+(bcd) -> (bcd)+a  : does not matter what ops are inside as
                      + is low precedence
 
a-(bcd) -> nothing! : What kind of expression would you need
                      inside parens to get 24 by subtracting
                      to 0..9?? Yes, I know that 0-(-something)
                      will be positive, but we can't have another
                      negative number inside the parens!!!
{edit} Actually, we can, but it does not create a solution! {/edit}
{edit} And it can be rewritten as not to need the parens! {/edit}
 
a/(bcd) -> nothing! : Again, what kind of number would we need
                      inside parens to get 24? A very small number!
                      In order to be so, we'd need something like
                      a/(b/c/d) because a/(b+c/d) or a/(b/c+d) would
                      not give a number below 1 unless the added item
                      was 0 and even then it would not be "small enough"
                      to get 24... (hope you're still following me!)
                      If we did not use a / inside the parens, then
                      the number would not be between 0 and 1 and so,
                      dividing a number from 1 to 9 by it would not
                      yield the needed result! Finally, a/(b/c/d) can
                      be simplified as a/b/c/d !!!
 
a*(bcd) -> (bcd)*a  : We will arrive at this test case sooner or later!
                      So, no need to handle it in here.
 
Please check my assumptions, but I do believe that a(bcd) can be safely
left out of the game as we're not trying to get ALL solutions but just
ONE!

---

quote:

---

Madruga

What about 8/(1*1/4)?

---

code:

---

$a='cdbl(8)/(cdbl(3)-cdbl(8)/cdbl(3))'
$rc=Execute("$$b=$a")
? 'Result $$b    = '$b
? 'Result 24=$$b = '+(24=$b)
? 'Result $$b=24 = '+($b=24)
? 'Result type  = '+VarTypeName($b)

---

code:

---

Result $b    = 24
Result 24=$b = 1
Result $b=24 = 0
Result type  = Double

---

Does anyone have an explaination for this behaviour???

code:

---

  13 (unlucky number!) depend on having two sets of (), that is (ab)(cd)
 131 depend on having at least one '+'
 174 depend on having at least one '-'
 306 depend on having at least one '*'
  36 depend on having at least one '/'

---

By now, it's clear to you guys: I was trying to simplify the algorithm by not including something!!!

Just thought to share my findings with you guys. Haven't coded a single KiXtart line yet...

[ 18. September 2002, 01:09: Message edited by: Fernando Madruga ]

code:

---

   0 need (ab)cd
   0 need a(bc)d
   0 need ab(cd)
------------------
   1 need (abc)d
------------------
   3 need a(bcd)
  13 need (ab)(cd)
------------------
 131 need at least one '+'
 174 need at least one '-'
 306 need at least one '*'
  36 need at least one '/'

---

So, and for the purpose of this game that is to find ONE
(repeat: ONE) solution, we can eliminate these constructs:
(ab)cd, a(bc)d, ab(cd).

The (abc)d construct is only used for these numbers
(and respective permutations): 1277 == (7*7-1)/2.

The a(bcd) construct is needed for these 3 sets:
1346 == 6/(1-3/4); 1456 == 6/(5/4-1); 1668 == 6/(1-6/8)

As for the (ab)(cd), 13 is too much to test for...
Even 3 may prove to be too much!

Hope this helps you guys, even though I may be shooting myself in the foot,
but hey! this is just a friendly competition...

Gonna do some work, then sleep over it. I'll probably only get back to this
in some 48 hours or so to start (and finish) my coding for this one, so
don't be surprised if you don't read from me for a couple of days...

[ 18. September 2002, 17:31: Message edited by: Fernando Madruga ]