special numbers question??????

khanna_sumit · **special numbers question?????? -** 22-04-2005, 12:48 PM

Call a positive real number

special if it has a decimal representation that consists entirely of digits 0 and 7. For example, 700/99 = 7.07..... = 7.070707 . . . and 77.007 are special numbers. What is the smallest n such that 1 can be written as a sum of n special numbers?

Eccentric · 22-04-2005, 01:05 PM

Here I smell that 999999 is dvisible by 7 i.e 142857*7
lets say A=999999

hence, (700000/A)*1 + (70000/A)*4 + (7000/A)*2 + (700/A)*8 + (70/A)*5 + (7/A)* 7 = 1

so Can be written by sum of 1+4+2+8+5+7 = 27 numbers !
may I find a better answer I'll post back

khanna_sumit · **incorrect.... -** 22-04-2005, 01:51 PM

Quote:

Originally Posted by Eccentric

Here I smell that 999999 is dvisible by 7 i.e 142857*7
lets say A=999999

hence, (700000/A)*1 + (70000/A)*4 + (7000/A)*2 + (700/A)*8 + (70/A)*5 + (7/A)* 7 = 1

so Can be written by sum of 1+4+2+8+5+7 = 27 numbers !
may I find a better answer I'll post back

u may have beenon the right track...i dont knowhow u have interpreted it as.....but ur answer is wrong....my questionwas that what is the minimum number of such special numbers which sum to 1.....

Eccentric · 22-04-2005, 02:02 PM

Quote:

Originally Posted by khanna_sumit

u may have beenon the right track...i dont knowhow u have interpreted it as.....but ur answer is wrong....my questionwas that what is the minimum number of such special numbers which sum to 1.....

I am telling you that according to me the minimum number of number as of now is 27. I even gave you a solution for how to get 1 by 27 special numbers !

khanna_sumit · **Hint..... -** 22-04-2005, 02:06 PM

Quote:

Originally Posted by Eccentric

I am telling you that according to me the minimum number of number as of now is 27. I even gave you a solution for how to get 1 by 27 special numbers !

ur answer is too large......actual answer is much lesser....

Eccentric · 22-04-2005, 02:12 PM

Quote:

Originally Posted by khanna_sumit

ur answer is too large......actual answer is much lesser....

I hope no negative nubers / subtraction are involved !

khanna_sumit · **hmmmmmmmmmmmmmm -** 22-04-2005, 02:22 PM

Quote:

Originally Posted by Eccentric

I hope no negative nubers / subtraction are involved !

all the numbers are +ve...........

khanna_sumit · **no answers?????????? -** 22-04-2005, 08:58 PM

Quote:

Originally Posted by khanna_sumit

Call a positive real number

special if it has a decimal representation that consists entirely of digits 0 and 7. For example, 700/99 = 7.07..... = 7.070707 . . . and 77.007 are special numbers. What is the smallest n such that 1 can be written as a sum of n special numbers?

if any 1 needs a hint, ask me or if u want to enjoy solving a question without any help thats ur choice.....