All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Get the bases! (Posted on 2018-10-17)
The number 1987 can be written as a three digit number xyz in some base b.
If x + y + z = 1 + 9 + 8 + 7=25, determine all possible values of x, y, z, b.

 See The Solution Submitted by Ady TZIDON No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer soln | Comment 1 of 5
Well, the only shortcut I saw was that 13<b<45 to give a three digit number with x non-zero. I tried by hand up to b=15 and then fell back to the computer. Base 19 held the answer:

5  9 11 base   19 adds to 25

I am painfully aware that these kids had no computers - so how did they limit the choices?

program zzz

do 2 i=13,45

ix=1987/i**2

is=1987-ix*i**2

iz=is-is/i*i

end

rabbit-3:~ lord\$ zzz

5  9 11 base   19 adds to 25
note, for x=0, looping up to base 2000, these work too:

rabbit-3:~ lord\$ zzz

0 18  7 base  110 adds to 25

0  9 16 base  219 adds to 25

0  6 19 base  328 adds to 25

0  3 22 base  655 adds to 25

0  2 23 base  982 adds to 25

0  1 24 base 1963 adds to 25

Edited on October 17, 2018, 4:39 pm
 Posted by Steven Lord on 2018-10-17 10:41:26

 Search: Search body:
Forums (0)