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 2006-08-02, 08:28 #1 R. Gerbicz     "Robert Gerbicz" Oct 2005 Hungary 72·31 Posts 2006 Create formulas using the same digit that evaluate 2006. Only the 4 basic operations so +,-,*,/ are allowed and you can concatenate but no other operations are allowed so you can't use square root, factorial, decimal dot, parentheses... The problem is to find formulas for digit=1,2,3,...,9 that are using the fewest number of digits! One good formula, but not the shortest for digit=5 for example: 2006=555+555+555+555-555/5-555/5+5+5-5/5-5/5 so using 26 digits.
 2006-08-02, 10:05 #2 Kees     Dec 2005 22·72 Posts just a long shot as first effort: 2006 = 1111+1111-111-111+1+1+1+1+1+1 (20) 2222-222+2+2+2 = (10) 3333-3333/3 -333 +333/3 + 3 + 3 (18) 4444/4+4444/4 -444/4-444/4+4+4/4+4/4 (23) 5555/5+5555/5 -555/5-555/5+5+5/5 (21) 6666/6+6666/6 -666/6-666/6+6 (19) 7777/7+7777/7 -777/7-777/7+7-7/7 (21) 8888/8+8888/8- 888/8-888/8+8-8/8-8/8 (23) 9999/9+9999/9 -999/9-999/9+9-9/9-9/9-9/9 (25)
 2006-08-02, 10:12 #3 Kees     Dec 2005 22·72 Posts 4*4*4*4*4+4*4*4*4*4-4*4-4*4-4-4-4/4-4/4 (20)
 2006-08-02, 10:17 #4 Kees     Dec 2005 22·72 Posts 99*9+9999/9+9/9+9/9+9/9+9/9 (16)
 2006-08-02, 11:08 #5 Greenbank     Jul 2005 2×193 Posts 7*7*7*7-7*7*7-7*7-77/7+7+7/7 (15) 55*5*5+5*5*5*5+5+5/5 (11) 9*9*9+9*9*9+9*9*9-9*9-99-9/9 (15) Last fiddled with by Greenbank on 2006-08-02 at 11:29
2006-08-02, 13:05   #6
Uncwilly
6809 > 6502

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Aug 2003
101×103 Posts

29×349 Posts

Quote:
 Originally Posted by R. Gerbicz Only the 4 basic operations so +,-,*,/ are allowed and you can concatenate but no other operations are allowed so you can't use square root, factorial, decimal dot, parentheses...
I take this to mean that 55 would be out. Is this correct?

 2006-08-02, 14:12 #7 Kees     Dec 2005 22·72 Posts 8888-8*888+888/8+888/8 (16)
2006-08-02, 14:16   #8
victor

Oct 2005
Fribourg, Switzerlan

3748 Posts

Quote:
 Originally Posted by Uncwilly I take this to mean that 55 would be out. Is this correct?
Seems to be correct, so 5^5 should be written 5*5*5*5*5.
I see that parentheses aren't allowed, but there is a small trick if you want to use some : write in RPN

 2006-08-02, 14:17 #9 Kees     Dec 2005 22×72 Posts 4444/4+444+444+4+4-4/4 (15) 6666-6*666-666+6/6+6/6 (15)
 2006-08-02, 14:22 #10 Kees     Dec 2005 3048 Posts 3*333+3*333+3*3-3/3 (12)
 2006-08-02, 14:30 #11 Kees     Dec 2005 22·72 Posts 44*44+44+44/4+44/4+4 (13)

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