# Enigmatic Code

Programming Enigma Puzzles

## Puzzle 73: A division sum. Find the missing digits

From New Scientist #1124, 12th October 1978 [link]

[puzzle73]

### 2 responses to “Puzzle 73: A division sum. Find the missing digits”

1. Jim Randell 11 May 2017 at 8:34 am

There’s no text with puzzle, so I assume we are meant to solve it in the usual way.

There is a blank space at the end of the dividend, so the result is a decimal fraction with 1 decimal place. We consider the equivalent division with the dividend multiplied by 10 and an integer result.

Here is the run file for using the SubstitutedDivision() solver from the enigma.py library. (Which can be executed directly from the command line, or using enigma.run() in an interactive Python session). It executes in 799ms.

```#!/usr/bin/env python -m enigma -r

# solver to use
SubstitutedDivision

# digits stand for themselves
--assign=9,9
--assign=3,3
--assign=0,0

# the division sum to solve
"???9?0 / ?? = ????"

# the intermediate subtraction sums
"??? - ?? = ?"
"?9 - ?? = ??"
"??? - ??? = ?3"
"?30 - ??? = 0"
```

Solution: The division sum is 10097 ÷ 46 = 219.5.

2. Jim Randell 19 July 2017 at 2:20 pm

With the new SubstitutedDivision() implementation in the enigma.py library we don’t need to specify that literal digits stand for themselves (they always do with the new solver), so the run-file is even shorter.

The following run-file executes in 168ms.

```#!/usr/bin/env python -m enigma -r

# solver to use
SubstitutedDivision

# the division sum to solve
"???9?0 / ?? = ????"

# the intermediate subtraction sums
"??? - ?? = ?"
"?9 - ?? = ??"
"??? - ??? = ?3"
"?30 - ??? = 0"
```