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.)

re(3): Possible solution

| Comment 10 of 14 |

(In reply to re(2): Possible solution by broll)

Sorry - perhaps my formula is unclear. I use * for 1st multiply and then remove 0's.

(((( 999 * 95) * 99) * 108) * 8) * 5 = 9

( via 9495, 945, 126, 18)

broken down is:

999 x 95 = 94905 -->9495

9495 x 99 = 94005 --> 945

945 x 108 = 102060 --> 126

126 x 8 = 1008 --> 18

18 x 5 = 90 --> 9

-----

I haven't had time to study your math or B. Smith's, but I seemed to get the idea you thought 999 could not be reduced to a single digit.

Maybe we now agree that it can.

Cheers

- SL

Posted by Steven Lord on 2019-09-13 17:56:57

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