perplexus.info :: Just Math : He gave me S and asked for X

He gave me S and asked for X (Posted on 2023-05-23)

Last night a puzzle was presented to me by my friend, a mathematician a.k.a. W.G. i.e. the Wise Guy.
He said: "I provide you a number S which is the sum of my secret
3 digit number X and 2 two-digit numbers derived from X by erasing one of its digits.
S is a 3 digit number composed of distinct digits. I want you, using no computation aids, just your brains, pen and paper to solve my conundrum.

The sum is 439 - What is my original number?"

Needless to say it was solved in no time, you can treat it as a d1 entry and handle it p&p.

But it inspired the following generalization addressing the perplexus society, rather d3:

There are plenty of 3 digit numbers using 3 distinct digits in the range of 102 to 987 (i. how many?).
Ii. How many, if used as S in the puzzle will provide a valid and unique X?
iii. How many yield: no solution?
iv. How many, if any, 2 or more answers?

No Solution Yet Submitted by Ady TZIDON

Rating: 3.0000 (2 votes)

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

re: more findings -- revised statistics

Comment 4 of 4 |

(In reply to more findings by Larry)

I do have new statistics, correcting my old ones:

ctDistinct =

648

uniqueX =

noSoln =

multiSoln =

536

but this comes from previously counting such lines as

   135   112   112

as multisolution, rather than unique X. The new stats come from not entering a number into a cell if that number is already there.

Edited on May 23, 2023, 5:08 pm

Posted by Charlie on 2023-05-23 17:07:36

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 (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info