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Old 2005-09-29, 01:44   #23
Ken_g6
 
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Rogue: Good job! Your 38 beats what I had, which was (4!sq+4sq+4sq)/4sq. I haven't had a chance to look at the rest of the solutions posted since then.

Someone could probably modify the code I wrote to solve the "Generating 2005" puzzle (which is attached to a post in there) to solve this. I haven't looked at trying yet.

P.S. That site is actually the worst of three sites with spoilers I found with Google. That site also uses the illegal floor (integer part) function.
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Old 2005-09-29, 01:52   #24
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rogue: what do you mean by ()sqsq? If I read it as (()^2)^2, 4sqsq + 4! = 65560.
BTW: 82 still lacks a solution, as 4!/.4 + 4! - 4 = 80 /= 82

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Old 2005-09-29, 02:28   #25
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Rogue ,

There's a problem with many of your solutions:

4sqsq isn't 64, it's 256. But where you use that with three 4's or less, you can sub your 4sqsq with 4*4sq.

62 = (4sqsq - 4 -4)/4

89 = ((4!/4)sq-.4)/.4
90 = (4!/4)sq/.4
91 = ((4!/4)sq+.4)/.4

Last fiddled with by grandpascorpion on 2005-09-29 at 02:32
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Old 2005-09-29, 02:36   #26
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Oops. It must have been that beer I had this evening. I don't know what I was thinking.
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Old 2005-09-29, 02:59   #27
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One little trick:

If you can't find a solution, see if 256-x is possible

113 = 4sqsq - (4!sq-4)/4
118 = 4sqsq - (4!sq-4!)/4
135 = 4sqsq - (44/4)sq
156 = 4sqsq - (4/.4)sq

That's as far as I checked.
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Old 2005-09-29, 04:14   #28
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Just recognised that you can save a 4 in my solution for 63/65 addopting this: 63 = (4^2^2-4)/4 giving 67 = (4^2^2-4)/4+4
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Old 2005-09-29, 05:52   #29
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46 = (4!-4)/.4-4
54 = 4!/4+4!+4!
66 = (4!+4)/.4-4
130 = (4!+4!+4)/.4

smallest # w/o representation: 73
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Old 2005-09-29, 10:36   #30
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Glancing over the record, I saw that 154 has a 3 4's representation, so:
158 = 4!/(.4)^2+4+4

Last fiddled with by Wacky on 2005-10-03 at 22:13
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Old 2005-09-29, 12:09   #31
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73 = (4sqsq+(4!/4)sq)/4
127 = (4!sq-4)/4-4sq
139 = (4!sq-4)/4-4
147 = (4!sq-4)/4+4
159 = (4!sq-4)/4+4sq
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Old 2005-09-29, 12:28   #32
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Where is "75" ?

From above:
77 = (4 - 4/4)sqsq - 4
94 = (4/.4)sq - 4!/4
105 = (44/4)^2-4^2

Last fiddled with by Wacky on 2005-10-03 at 22:12
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Old 2005-09-29, 13:50   #33
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126 = (4!sq+4!)/4-4!
129 = (4!sq+4)/4-4sq
134 = (4!sq+4!)/4 - 4sq
137 = (4!sq-4!-4)/4
141 = (4!sq-4sq+4)/4

Last fiddled with by Wacky on 2005-09-29 at 14:32 Reason: Note: Now removed from pending list
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