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Old 2006-08-02, 08:28   #1
R. Gerbicz
 
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"Robert Gerbicz"
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Default 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.
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Old 2006-08-02, 10:05   #2
Kees
 
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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)
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Old 2006-08-02, 10:12   #3
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4*4*4*4*4+4*4*4*4*4-4*4-4*4-4-4-4/4-4/4 (20)
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Old 2006-08-02, 10:17   #4
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99*9+9999/9+9/9+9/9+9/9+9/9 (16)
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Old 2006-08-02, 11:08   #5
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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
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Old 2006-08-02, 13:05   #6
Uncwilly
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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?
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Old 2006-08-02, 14:12   #7
Kees
 
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8888-8*888+888/8+888/8 (16)
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Old 2006-08-02, 14:16   #8
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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
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Old 2006-08-02, 14:17   #9
Kees
 
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4444/4+444+444+4+4-4/4 (15)
6666-6*666-666+6/6+6/6 (15)
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Old 2006-08-02, 14:22   #10
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3*333+3*333+3*3-3/3 (12)
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Old 2006-08-02, 14:30   #11
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44*44+44+44/4+44/4+4 (13)
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