playing with numbers - Page 2

michael · 2004-01-16, 14:41

I'm surprised no one found the answer yet, base 15 is first base i couldn't find an answer for.

base 7: 3*4 + 1*6=24
base 8: 6*4 - 3 - 1=24
base 9: 6*4 - 3 + 1=24
base 10: 6/(1 - 3/4)=24
base 11: 6*4 + 3 - 1=24
base 12: 6*4 + 3 + 1=24
base 13: 3*1*(6 + 4)=24
base 14: (6 + 3 - 1)*4=24

-michael

mfgoode · 2004-01-16, 16:31

Dear michael, Excelent work. It set me thinking.
I didnt think fractions were allowed but even then it would be tough.
As a matter of interest this can be worked in factorial form;viz
4! *3!/6 *1 =24
Mally.

nfortino · 2004-01-16, 16:55

My illegal solution was (6*4)^1[sup]3[/sup]

tom11784 · 2004-01-17, 00:15

There is no solution for base 15 (equivalent of finding a solution for 34 in base 10)

I'm currently creating a list of all possible non-negative values possible with such arrangements of 1,3,4, and 6 in base 10 and shall post again when that is completed.

Interestingly enough, 34 is the smallest non-negative integer that fails this.

2004-01-16, 14:41	#12
michael Dec 2003 Belgium 41₁₆ Posts	I'm surprised no one found the answer yet, base 15 is first base i couldn't find an answer for. base 7: 34 + 16=24 base 8: 64 - 3 - 1=24 base 9: 64 - 3 + 1=24 base 10: 6/(1 - 3/4)=24 base 11: 64 + 3 - 1=24 base 12: 64 + 3 + 1=24 base 13: 31(6 + 4)=24 base 14: (6 + 3 - 1)4=24 -michael Last fiddled with by michael on 2004-01-16 at 14:44*

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2004-01-16, 16:31	#13
mfgoode Bronze Medalist Jan 2004 Mumbai,India 2²×3³×19 Posts	Dear michael, Excelent work. It set me thinking. I didnt think fractions were allowed but even then it would be tough. As a matter of interest this can be worked in factorial form;viz 4! 3!/6 1 =24 Mally.

2004-01-16, 16:55	#14
nfortino Nov 2003 3×5×11 Posts	My illegal solution was (6*4)^1[sup]3[/sup]

2004-01-17, 00:15	#15
tom11784 Aug 2003 Upstate NY, USA 101000110₂ Posts	There is no solution for base 15 (equivalent of finding a solution for 34 in base 10) I'm currently creating a list of all possible non-negative values possible with such arrangements of 1,3,4, and 6 in base 10 and shall post again when that is completed. Interestingly enough, 34 is the smallest non-negative integer that fails this.