20060802, 08:28  #1 
"Robert Gerbicz"
Oct 2005
Hungary
7^{2}·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+555555/5555/5+5+55/55/5 so using 26 digits. 
20060802, 10:05  #2 
Dec 2005
2^{2}·7^{2} Posts 
just a long shot as first effort:
2006 = 1111+1111111111+1+1+1+1+1+1 (20) 2222222+2+2+2 = (10) 33333333/3 333 +333/3 + 3 + 3 (18) 4444/4+4444/4 444/4444/4+4+4/4+4/4 (23) 5555/5+5555/5 555/5555/5+5+5/5 (21) 6666/6+6666/6 666/6666/6+6 (19) 7777/7+7777/7 777/7777/7+77/7 (21) 8888/8+8888/8 888/8888/8+88/88/8 (23) 9999/9+9999/9 999/9999/9+99/99/99/9 (25) 
20060802, 10:12  #3 
Dec 2005
2^{2}·7^{2} Posts 
4*4*4*4*4+4*4*4*4*44*44*4444/44/4 (20) 
20060802, 10:17  #4 
Dec 2005
2^{2}·7^{2} Posts 
99*9+9999/9+9/9+9/9+9/9+9/9 (16) 
20060802, 11:08  #5 
Jul 2005
2×193 Posts 
7*7*7*77*7*77*777/7+7+7/7 (15) 55*5*5+5*5*5*5+5+5/5 (11) 9*9*9+9*9*9+9*9*99*9999/9 (15) Last fiddled with by Greenbank on 20060802 at 11:29 
20060802, 13:05  #6  
6809 > 6502
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Aug 2003
101×103 Posts
29×349 Posts 
Quote:


20060802, 14:12  #7 
Dec 2005
2^{2}·7^{2} Posts 
88888*888+888/8+888/8 (16) 
20060802, 14:16  #8  
Oct 2005
Fribourg, Switzerlan
374_{8} Posts 
Quote:
I see that parentheses aren't allowed, but there is a small trick if you want to use some : write in RPN 

20060802, 14:17  #9 
Dec 2005
2^{2}×7^{2} Posts 
4444/4+444+444+4+44/4 (15) 66666*666666+6/6+6/6 (15) 
20060802, 14:22  #10 
Dec 2005
304_{8} Posts 
3*333+3*333+3*33/3 (12) 
20060802, 14:30  #11 
Dec 2005
2^{2}·7^{2} Posts 
44*44+44+44/4+44/4+4 (13) 
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