# Enigmatic Code

Programming Enigma Puzzles

## Puzzle 2: Two, three, four, six

From New Scientist #1052, 26th May 1977 [link]

In this long division sum, I fear,
Most of the figures simply are not there.
Two and Three and Four and Six,
One of these is wrong. But which?
Three and Six and Four and Two,
Do you think that’s much too few?
Why don’t I give you rather more,
Than Six and Two and Three and Four?
To give you four, you will agree,
Is better than to give you three.
Look at the pattern if you wish.
All the figures look like this:

Which figure was wrong? Find the correct division sum.

#### News

This completes the Puzzle series of puzzles that were originally published in New Scientist between May 1977 (when Tantalizer finished) and February 1979 (when Enigma started).

There is now a complete archive of puzzles from July 1975 up to December 1989, and from March 1998 to December 2013 (when Enigma finished). Making a grand total of around 1542 puzzles on the site (plus a few extra) – about 30 years worth!

I will continue posting Enigma puzzles on Monday and Friday, and Tantalizer puzzles on Wednesday.

[puzzle2]

## Puzzle 3: Letters for digits

From New Scientist #1053, 2nd June 1977 [link]

In the addition sum below letters have been substituted for digits. The same letter stands for the same digit wherever is appears, and different letters stand for different digits.

Write the sum out with numbers substituted for letters.

[puzzle3]

## Puzzle 4: Football (4 teams. Old method)

From New Scientist #1054, 9th June 1977 [link]

Four football teams, A, B, C and D, are to play each other once. After some — or perhaps all — of the matches have been played a table giving some details of matches played, won, lost, etc, looked like this:

(2 points are given for a win and one point to each site in a drawn match).

Find the score in each match.

[puzzle4]

## Puzzle 5: “I would if I could”

From New Scientist #1056, 16th June 1977 [link]

“I would if I could, but I’m sorry I can’t.”
I felt that I had to say this to my Aunt.
She seemed to expect me to lend her some cash.
And knowing my Aunt that would surely be rash.
I happen to know what her overdraft is;
My Uncle’s is large, hers is much more than his.
Her husband, my Uncle, in fact owed the bank
A number of pounds which was, let’s be frank,
Sixty-three more than my overdraft then.
Aunty’s and mine are two-hundred-and-ten;
Between them, I mean, and I’d like you to see,
When I say “much”, Aunt’s is Uncle’s times three —
Or as near to three as it can be,
Bearing in mind this vital fact:
The pounds we owe are all exact.

What are the overdrafts of my Aunt, my Uncle and myself.

This puzzle was later re-published as Enigma 182.

[puzzle5]

## Puzzle 6: On the silly side of Silly Street

From New Scientist #1057, 23rd June 1977 [link]

On the Island of Imperfection there are three tribes, the Pukkas who always tell the truth, the Wotta-Woppas who never tell the truth, and the Shill-Shallas who make statements which are alternately true and false (or false and true).

The four inhabitants of the Island with whom this story deals live in separate houses all on one side of Silly Street where the numbers of the houses are all odd, from 1 to 41 inclusive.

They speak as follows:

A.1: D’s number is one third of C’s;
A.2: D is a Wotta-Woppa.

B.1: The numbers of all our four houses are multiples of 5;
B.2: C’s number is less than A’s.

C.1: A belongs to the same tribe as I do;
C.2: A Pukka lives in No 35.

D.1: C’s number is greater than B’s;
D.2: B belongs to a more truthful tribe than I do.

You are told that there is at least one representative from each tribe, but only one Shilli-Shalla.

Find their tribes and the numbers of their houses.

[puzzle6]

## Puzzle 7: The Woogle on the wardrobe

From New Scientist #1058, 30th June 1977

I thought Professor Knowall looked at me rather strangely as I came into the office one day.

“You don’t look, my dear Sergeant Bungle”, he said, “as though you have had a very good night’s sleep”.

I was amazed by his perception. In a flash he had seen not only that I was not feeling quite myself, but also why. The least I could do, I felt, was to give him more information about the sleepless night thats I had been having.

The last few nights had been rather windy. I had heard, as I lay in bed, an intermittent high-pitched squeak, and a regular dull thud.

I got out of bed, clasped with one hand the woogle that hangs outside my wardrobe and with the other the chumph that is loose on the top of my chest of drawers, and steadied with my foot the pollux, which is normally free to move around the floor on casters. The thud stopped, but the squeak continued.

I kept hold of the chumph, seized with my other hand the Venetian blind, and transferred my foot to the rocking chair. The squeak stopped and there was still no thud.

I then kept hold of the Venetian blind, seized the woogle once more and took my foot off the rocking chair. The thud started up again, but there was no squeak.

But what could I do? I know that the Professor would approve of my making these experiments, but not many can control woogles, chumphs, polluxes’, Venetian blinds and rocking chairs, all at once, and I had been unable to come to any conclusions as to what caused the noises.

The professor, with the information that I had given him, solved the problem in less time than it takes to steady a pollux with a foot.

What can you say about the causes of the two noises?

Happy Christmas from Enigmatic Code!

[puzzle7]

## Puzzle 8: Division (letters for digits)

From New Scientist #1059, 7th July 1977 [link]

In the following division sum each letter stands for a different digit:

Re-write the sum with the letters replaced by digits.

[puzzle8]

## Puzzle 9: The boss’s birthday

From New Scientist #1060, 14th July 1977 [link]

I could not help overhearing an argument the other day between my seven employees, Alf, Bert, Charlie, Duggie, Ernie, Fred and George about the month in which my birthday is. I must admit that I was rather interested in this, for it seemed to be connected with a suggestion about recognising it in some way.

The conversation between them took place on 1st May and it went as follows:

Alf: I have heard him say how wonderful it was having a birthday in a month that started with one of the two letters in the middle of the alphabet. He seems to me rather to over-estimate the advantages of that. In fact I think he is crazy!

Bert: His birthday is not this month or next, but either the one after that or the one after that.

Charlie: I have often heard him say what a disadvantage it has been having a birthday so close to Christmas. This means, I am sure, that it is within two months either way.

Duggie: He told me some time ago that his birthday is in a month with only 30 days.

Ernie: I asked him only the other day and he said it was in October.

Fred: I know that it is not in the winter — i.e. in the last three months or the first three months of the year.

George: You are too late this year; he has had his birthday already.

In fact only one of those statements was true. Which one? Can you say in which month my birthday is? If so, when?

[puzzle9]

## Puzzle 10: A cross number

From New Scientist #1061, 21st July 1977 [link]

(There are no 0’s)

Across:

1. Half of 2 down.
3. Each digit is 2 greater than the one before.
4. The sum of the digits is at least 3 greater than the sum if the digits of 1 across.

Down:

1. The 1st digit is greater than the 2nd digit by the same amount as the 2nd digit is greater than the 3rd digit.
2. Twice 1 across.
3. An odd number

[puzzle10]

## Puzzle 11: Cricket (4 teams (6))

From New Scientist #1062, 28th July 1977 [link]

In a cricket competition 4 teams — A, B, C and D — all play each other once.

Points are awarded as follows:

To the side that wins: 10
To the side that wins on the first innings in a drawn match: 6
To the side that loses on the first innings in a drawn match: 2
To each side for a tie: 5
To the side that loses: 0

A, B, C and D get 16, 11, 21 and 6 points respectively, and you are told that A won one match.

Find the result of each match.

[puzzle11]

## Puzzle 12: The puzzle of life

From New Scientist #1063, 4th August 1977 [link]

I wish I knew what life was for,
For many years I’ve wondered;
It is a puzzle; more and more
It seems that someone’s blundered.

A puzzle, yes — so that’s what life’s about;
So I will concentrate my tiny mind
On solving just a single one of them.
Two brothers and their ages I must find.

A is twice as old as B
Will be in ten years time.
And it is true that when B is
Three times what A was when,
Twenty one years ago, his age was such
That he was still a minor, (old or new —
But not aged less than ten),
Then the two digits of his age will add to nine.
Which will be fine.
If you know who’s “he”. “I, there’s the rub”.
Shakespeare, of course, or I might say
That there’s the rubber-dubber-dub!

But use your reason and you will discover
A’s age a present and that of his brother.
(One thing I ought to add. They have a clever mum.
Both their birthdays are to-day, that makes an easy sum).

What are A’s and B’s ages?

[puzzle12]

## Puzzle 13: A diversity of scores

From New Scientist #1064, 11th August 1977 [link]

4 football teams, A, B, C and D are all to play each other once. After some, or perhaps all, the matches had been played, I discovered that 18 goals had been scored altogether and that B has scored 2 more than each of the other three. B also had three times as many goals scored against them as D had, and A had the same number of goals against them as for them. C had fewer goals scored against them than anyone else.

It was interesting to notice that in every match both sides scored at least 1 goal, and that in no matches were the scores exactly the same. One match was drawn.

Find the score in all the matches that were played.

[puzzle13]

## Puzzle 14: Our factory has a holiday outing

From New Scientist #1065, 18th August 1977 [link]

With the increasing standard of living, the members of my factory think more and more of the delights of abroad. And once they have tasted these delights there is no place to which they would rather go than the Island of Imperfection, where lies can be told proudly and as of right, as they were in the golden age.

There are three tribes on this Island — the Pukkas who always tell the truth, the Wotta Woppas who never tell the truth, and the Shilli Shallas who make statements which are alternately true and false (or false and true). This story deals with four members of our Factory: Alf, Bert, Charlie and Duggie, whose jobs — not necessarily respectively — were, when they were last working in this country, those of: Door-Opener, Door-Shutter, Welfare Officer and Bottle Washer. Each of the three tribes has at least one representative, but I am afraid I can give no more information about the tribe to which the fourth man belongs.

The make statements as follows:

Alf:
(1) The Welfare Officer is a Wotta Woppa;
(2) Only one of us is a Pukka.

Bert:
(1) Alf is a Pukka;
(2) Charlie is the Welfare Officer.

Charlie:
(1) I am a Wotta Woppa;
(2) Duggie is the Door-Shutter.

Duggie:
(1) The Door-Opener is a Shilli Shalla;
(2) Charlie is not a Wotta Woppa.

Find the jobs which Alf, Bert, Charlie and Duggie had when they were last in this country, and the tribes to which they belong on the Island of Imperfection.

[puzzle14]

## Puzzle 15: Pay claims

From New Scientist #1066, 25th August 1977 [link]

We have recently started on the Island of Imperfection to build up a modern society. We have come to realise some of the inestimable advantages that a pay claim, with all its colour and friendly disagreements, can bring to life.

There are three tribes on the Island. The Pukkas, who always tell the truth, the Wotta Woppas, who never tell the truth, and the Shilli-Shallas who make statements which are alternately true and false, or false and true. Our story deals with one representative from each tribe.

Psychologists of the future may learn much about thinking on the Island at this time from the simple fact that the main units of currency were called Hopes, and that a Hope was made up of 100 Fears.

The three (AB and C) speak about their tribes and wages:

A:
(1) My wages are greater than B‘s;
(2) The weekly bill for wages (of A, B and C) is 80 Hopes;
(3) C is a Shilli-Shalla.

B:
(1) A is a Pukka;
(2) A‘s wages are six Hopes less than mine;
(3) The weekly bill for wages (of A, B and C) is 92 Hopes.

C:
(1) My wages are not a multiple of five Hopes;
(2) A‘s wages are nine Hopes greater than mine.

(Their wages are all different and are greater than 20 Hopes and less than 35 Hopes per week; and in each case they are exact multiples of 50 Fears).

Find to which tribe each man belongs, and his weekly wage.

[puzzle15]

## Puzzle 16: Addition. Digits all wrong

From New Scientist #1067, 1st September 1977 [link]

Each digit in the addition sum below is wrong. But the same wrong digit stands for the same correct digit wherever it appears, and the same correct digit is always represented by the same wrong digit.

[puzzle16]

## Puzzle 17: Goals rewarded

From New Scientist #1068, 8th September 1977 [link]

A lot of people have been of the opinion for some time that in football competitions some importance should be attached to the number of goals scored as well as to the actual result of the game. It is hoped that this will lead to more goals and therefore to more attractive games.

Three local teams of my acquaintance have been experimenting on these lines. The have had a competition in which they all played each other once, and they have awarded ten points for a win, five points for a draw, no points of course for a loss, and one point for each goal scored.

As a result of this competition one team scored 16 points, the second scored 18 points, and the third scored 10 points. It was interesting to notice that at least one goal was scored by both sides in every match.

What was the score in each match?

[puzzle17]

## Puzzle 18: Division (letters for digits)

From New Scientist #1069, 15th September 1977 [link]

In this division sum each letter stands for a different digit. Rewrite the sum with the letters replaced by digits.

[puzzle18]

## Puzzle 19: Cross number

From New Scientist #1070, 22nd September 1977 [link]

(There are no 0’s).

Across:

1. Sum of digits is 12.
3. A prime number.
5. Each digit is greater than the one before.
7. Digits all even and different; in either ascending or descending order.
8. Digits all odd and all different.
9. The sum of the digits is less than the sum of the digits of 1 across.
10. The product of 2 primes.

Down:

1. A multiple of cube root of 6 down.
2. The sum of the digits is 24.
3. The square of a number, followed by the number itself.
4. The same when reversed.
6. A perfect cube.
8. Even.

When the puzzle was originally published there was a typo in the clue for 1 across (corrected here).

I have also changed the clue for 10 across. Originally it read: “A multiple of 2 primes”.

[puzzle19]

## Puzzle 20: “I do not wish to be, I’d like to add”

From New Scientist #1071, 29th September 1977 [link]

I do not wish to be,
Being is a matter of degree,
I know this well,
But my decision just to be no more
It comes from an experience of life second to none.
It means that I have said, no love, no laughter,
Mechanisation’s what I want and see what follows after.
It leads to certainty, and that is what I have a passion for,
“Why yes, perhaps it is, perhaps it is not”, no more, no more.
For now the great adventure, the hour when I cease to exist,
And just become a computer, no life but also no risk.
Perhaps you this my no-life has no future.
To show you’re wrong I offer you a test.
Letters for digits, add something to “COMPUTER”
And you will find certainty, peace and rest.

Write the sum out with numbers substituted for letters.

[puzzle20]

## Puzzle 21: Cricket (4 teams)

From New Scientist #1072, 6th October 1977 [link]

A, B, C and D have all played each other once at cricket.

Points are awarded as follows:

To the side that wins — 10
To the side that wins on the first innings in a drawn match — 6
To the side that loses on the first innings in a drawn match — 2
To each side for a tie — 5
To the side that loses — 0

A, B, C and D got 10, 11, 17 and 14 points respectively, and you are told that only one match was won outright.

Find the result of each match.

[puzzle21]