## Teaser 2949: Mystery numbers

**From The Sunday Times, 31st March 2019** [link]

I wrote down a 2-digit number and a 5-digit number and then carried out a long division.

I then erased all of the digits in the calculation, other than one of them, which I have indicated by X.

This gave me the image above.

What were my two original numbers?

[teaser2949]

## Jim Randell 8:15 am

on31 March 2019 Permalink |We can feed this problem directly to the [[

`SubstitutedDivision()`

]] solver from theenigma.pylibrary.This run file executes in 153ms.

Run:[ @repl.it ]Solution:The two original numbers were: 23 and 33603.LikeLike

## Jim Randell 4:32 pm

on31 March 2019 Permalink |Although the run file given above does find the correct answer, which can be verified by inspection. I think there is a little bit more work to do to ensure that the erased digits are all different from the digit X.

Here is a run file that uses symbols for the erased digits (instead of the wildcard “?”), and includes an extra check to make sure they are all different from X.

LikeLike

## GeoffR 12:34 pm

on21 April 2019 Permalink |LikeLike