perplexus.info :: Numbers : Reduced to single digit

Reduced to single digit (Posted on 2019-09-06)

Suppose that we have two operations that we can perform on an integer:

Multiply it by any positive integer.
Delete the 0's in its decimal representation.

Beginning with any positive integer can we always obtain a single-digit number after a finite number of operations? For example, beginning with 7, we can multiply by 15 to obtain 105, delete the 0 to get 15, multiply by 2 to get 30, then delete the 0 to end with 3.

No Solution Yet Submitted by Danish Ahmed Khan

Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

regarding 111, etc.

Comment 14 of 14 |

(In reply to re(4): Possible solution by Charlie)

This I find interesting:

((((( 111 * 98^2) * 5^4 ) * 12^2) * 4^2) *5^2) * 5 = 9

(((( 999 * 11^2 ) * 4^2 ) * 2^2 ) * 5^3 ) * 2^2) * 5 = 9

multiplying by powers of integers (powers 2 and greater) and then by 5 seems always sufficient but not necessary.

Edited on September 14, 2019, 6:36 pm

Posted by Steven Lord on 2019-09-14 15:14:16

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (14)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info