﻿ Enigma Problems from “New Scientist" Magazine

# Programmed Solutions to "Enigma" Problems from New Scientist Magazine

The British weekly New Scientist includes a regular feature called "Enigma" that presents a short mathematical problem. Readers are invited to submit solutions, and on a stated date, one is drawn and awarded £15.

For years I have been somewhat annoyed at these problems because most of them seem to lend themselves to "brute force" solutions easily solvable by a short computer program. I usually know what the particular program needs to do and how to do it, so without actually writing a line of code (or doing anything else to solve the problem), I consider the problem "solved" nevertheless.

However, it has recently occurred to me that these computer solutions to the "Enigma" problems might be of interest in themselves in illustrating useful algorithms or programming techniques. For each "Enigma" problem I take on, I will post a solution and the program I used to determine that solution on the day after the deadline for submitting solutions.

Programs are written in ANSI C, and have been tested with the Microsoft C compiler and the Gnu C compiler. They make use only of the C standard libraries. I make no claims that these solutions are the fastest or most efficient, or even that they work correctly. When the answers are printed in the magazine (6 issues after the problem), the Postscript column below will indicate whether I got the right answer or what went terribly wrong.

Charles Petzold
17 June 2005

March 3, 2006: Due to work pressures, I won't be able to continue this project.

Problem Number Issue Date Solution Posted Solution Program Postscript
1378
Exaudi Deus
11 February 2006 16 March 2006 64 enigma1378.c
1376
Square Facts and Faces
28 January 2006 2 March 2006 9 faces, 4 triangles enigma1376.txt
1374
Dominoes to the Power of Two
14 January 2006 16 February 2006 0-6, 1-1, 3-3, 4-4, 6-6  enigma1374.c Wrong!
(Issue of 2/25 says
1-1, 2-2, 3-3, 5-5, 0-2)
1373
From Point to Corner
7 January 2006 9 February 2006 21 and 28 enigma1373.txt Correct
(Issue of 2/18)
1372
Three Tours
24/31 December 2005 2 February 2006 Bethlehem to Hebron by Ass enigma1372.c Correct
(Issue of 2/11)
1371
Odd Big Base
17 December 2005 26 January 2006 30 enigma1371.c Correct
(Issue of 2/4)
1370
10 December 2005 19 January 2006 11 cm enigma1370.c Correct
(Issue of 1/28)
1369
Magic Spell
3 December 2005 12 January 2006 JULY, FORD, MAINE, TWO, NINE enigma1369.txt Correct
(Issue of 1/21)
1368
Dutch Squares
26 November 2005 5 January 2006 144,837 enigma1368.txt Correct
(Issue of 1/14)
1367
19 November 2005 21 December 2005 33, 32, 31,
19, 9, and 1
enigma1367.c Wrong!
(Issue of 1/7 says
37, 39, 13, 3, 2, 1
1366
Done in Half the Time
12 November 2005 15 December 2005 9:49 PM enigma1366.c Correct
(Issue of 12/24 & 31)
1365
European Champions Leagues
5 November 2005 8 December 2005 8 enigma1365.c Correct
(Issue of 12/17)
1364
Four All
29 October 2005 1 December 2005 4096, 4567,
4936, 8164
enigma1364.c Correct
(Issue of 12/10)
1363
Hat Stand
22 October 2005 24 November 2005 PQSRT enigma1363.txt Correct
(Issue of 12/3)
1362
Eight-Fifths
15 October 2005 17 November 2005 1260 Miles enigma1362.c Correct
(Issue of 11/26)
1361
Enigma Variation
8 October 2005 10 November 2005 785,463 enigma1361.c Correct
(Issue of 11/19)
1360
An Enigma Gem
1 October 2005 3 November 2005 GEMNAI enigma1360.c Correct
(Issue of 11/12)
1359
The Weaker Sex
24 September 2005 27 October 2005 5 couples;
no games
enigma1359.c Correct
(Issue of 11/5)
1358
Five Fives
17 September 2005 20 October 2005 88,724 enigma1358.c Correct
(Issue of 10/29)
1357
Diminishing Powers
10 September 2005 13 October 2005 2, 9, and 10,
then 1 and 5
enigma1357.c Correct
(Issue of 10/22)
1356
Magic Spot
3 September 2005 6 October 2005 1-0 3-0 5-0
6-0 3-3 6-5
enigma1356.c Correct
(Issue of 10/15)
1355
Cube Words
27 August 2005 30 September 2005 cfe afd efa enigma1355.c Correct
(Issue of 10/8)
1354
Sound Idea
20 August 2005 23 September 2005 10,145,892,367 enigma1354.c Correct
(Issue of 10/1)
1353
Three Cubed
13 August 2005 16 September 2005 4096
8
729
2
1331
enigma1353.c Correct
(Issue of 9/24)
1352
All But One
6 August 2005 9 September 2005 32 enigma1352.c Correct
(Issue of 9/17)
1351
Let's Face It
30 July 2005 2 September 2005 210 enigma1351.c Correct
(Issue of 9/10)
1350
All But One
23 July 2005 25 August 2005 3754 enigma1350.c Correct
(Issue of 9/3)
1349
Alphabetic Magic
16 July 2005 19 August 2005 45 and 21 enigma1349.c Correct
(Issue of 8/27)
1348
Team Promotions
9 July 2005 12 August 2005 35 enigma1348.c Correct
(Issue of 8/20)
1347
Fair and Square
2 July 2005 5 August 2005 D = 21
U = 18
R = 4
enigma1347.c Correct
(Issue of 8/13)
1346
Divide into Primes
25 June 2005 29 July 2005 131p enigma1346.c Correct
(Issue of 8/6)
1345
Score? Date?
18 June 2005 22 July 2005 Scores are
A-D, B-C, C-D
enigma1345.c Correct
(Issue of 7/30)
1344
Mixed Pairs
11 June 2005 15 July 2005 Miss Take's: 14
Miss Giving's: 12
enigma1344.c Wrong
(Issue of 7/23 says
12 and 10.)
1343
Digital Dividend
4 June 2005 8 July 2005 9,867,312 enigma1343.c Correct
(Issue of 7/16)
1342
GOSH
28 May 2005 1 July 2005 33 pins enigma1342.c Correct
(Issue of 7/9)
1341
Two, Three, Four
21 May 2005 24 June 2005 THREE=15400
FOUR=6724
enigma1341.c Correct
(Issue of 7/2)
1340
Stairs and Sums
14 May 2005 17 June 2005 15.17 enigma1340.c Basically correct:
(Issue of 6/25 says
38231 / 2520)