### Random Post

### Recent Posts

### Recent Comments

### Archives

### Categories

- article (11)
- enigma (1,367)
- misc (4)
- project euler (2)
- puzzle (90)
- puzzle# (48)
- site news (58)
- tantalizer (94)
- teaser (7)

### Site Stats

- 233,130 hits

Programming Enigma Puzzles

12 October 2013

Posted by on **From New Scientist #2544, 25th March 2006**

I have drawn a grid of five rows of nine boxes and have placed in each box a digit so that each digit occurs its own number of times (e.g. 4 occurs four times). The digits in one row form a number which is a fourth power, and another row contains only two different digits and is divisible by 33. Two other rows between them contain all the digits and are both fifth powers.

In ascending order, what are the nine digits occupying the remaining row?

[enigma1384]

%d bloggers like this:

This program looks for one arrangement of the number composed of only two different digits (as “anagrams” of this number won’t change the overall solution). It runs in 38ms.

Solution:The digits in the remaining row are: 3, 4, 5, 5, 8, 8, 8, 8, 8.There are, in fact, 30 possibilities for the number composed of only two different digits, but the 4th and 5th powers are unique.