Enigmatic Code

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Category Archives: puzzle

Puzzle 25: Body and soul

From New Scientist #1076, 3rd November 1977 [link]

I have been trying to persuade my employees at Our Factory of the merits, whatever Shakespeare’s Julius Ceasar may have said, of an honest soul in a slim body; and the connection between weight and truth. Alf, Bert, Charlie and Duggie have become particularly weight conscious and they were making some remarks one day about the latest news the scales had given them.

They spoke as follows:

Alf: Bert is lighter than Duggie.
Bert: Alf is heavier than Charlie.
Charlie: I am heavier than Duggie.
Duggie: Charlie is heavier than Bert.

I found it interesting to note that my theory was supported. In fact the only one of these remarks to be true was that made by the lightest of the four men (their weights were all different).

Arrange Alf, Bert, Charlie and Duggie in order of weight.

[puzzle25]

Puzzle 26: Some old men on The Island of Imperfection

From New Scientist #1077, 10th November 1977 [link]

There are three tribes on The Island of Imperfection, the Pukkas who always tell the trith, 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 men whom we shall call ABC, and D and there is at least one representative of each tribe among them.

They make statements in accordance with their tribal characteristics as follows:

A:
(1) My age is a multiple of six;
(2) My age is not the same as B‘s age;
(3) D belongs to a more truthful tribe than I do.

B:
(1) I am older than A;
(2) The ages of A and C are the same;
(3) D‘s age is a multiple of twelve.

C:
(1) I am older than A;
(2) D‘s age is even;
(3) B‘s second remark is true.

D:
(1) B is three times as old as C;
(2) My age is twelve more than A‘s age;
(3) C‘s age is a multiple of thirteen.

People tend to live for a long time on this wonderful island, but none of the four with whom this story deals is older than 105.

Find the tribes to which each man belongs, and their ages.

[puzzle26]

Puzzle 27: Addition (letters for digits – 2 numbers)

From New Scientist #1078, 17th November 1977 [link]

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

Write the sum out with numbers substituted for letters.

[puzzle27]

Puzzle 28: Cross number

From New Scientist #1079, 24th November 1977 [link]

Across:

1. Three of these digits are those of 6 across, not necessarily in the same order, and the other one is the sum of the digits of 6 across.
5. A multiple of the square root of 7 down.
6. A perfect cube.
8. A multiple of 23.
9. This is a prime number when reversed.
10. Each digit is greater than the one before.
12. The sum of the digits is 12.

Down:

1. The sum of the digits of this number is the same as the sum of the digits of 3 down.
2. The same when reversed.
3. See 1 down.
4. Each digit is greater than the one before.
7. A perfect square.
8. A multiple of 19.
11. A prime number.

[puzzle28]

Puzzle 29: Division (letters for digits)

From New Scientist #1080, 1st December 1977 [link]

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

Rewrite the sum with the letters replaced by digits.

[puzzle29]

Puzzle 30: Football – new method (3 teams)

From New Scientist #1081, 8th December 1977 [link]

A new method to encourage goals in football matches has been suggested. In this method 10 points are awarded for a win, five points for a draw and one point for each goal scored whatever the result of a match.

3 teams, A, B and C are all to play each other once. After some, or perhaps all, of the matches have been played the points were as follows:

A   3
B   7
C  21

Not more than 7 goals were scored in any match.

What was the score in each match?

[puzzle30]

Puzzle 31: Division. Figures all wrong

From New Scientist #1082, 15th December 1977 [link]

In the following, obviously incorrect, division sum the pattern is correct, but every single figure is wrong.

puzzle-31

Find the correct figures. (The correct division comes out exactly. All the digits in the answer are only 1 out, but all the other digits may be incorrect my any amount).

[puzzle31]

Puzzle 32: Cricket (4 teams)

From New Scientist #1083, 22nd December 1977 [link]

ABC and D are all to play each other once at cricket. After some — or possibly all — the matches have been played, A had got 18 points, B had got 17 and C had got 21. I’m afraid however, that I was not able to find out how many points D had got.

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.

Find the results of all the matches that were played.

[puzzle32]

Puzzle 33: Football and addition (Letters for digits)

From New Scientist #1084, 5th January 1978 [link]

In the following football table and addition sum, letters have been substituted for digits (from 0 to 9). The same letter stands for the same digit wherever it appears, and different letters stand for different digits.

puzzle-33

(2 points are given for a win and 1 point to each side in a drawn match).

Find the scores in the football matches, and write out the addition sum with numbers substituted for letters.

This completes the archive of puzzles from 1978. There is now a full archive of puzzles from New Scientist from January 1978 to September 1988, and also from May 1999 up to the final Enigma puzzle in December 2013. Together with the Tantalizer puzzles from Mar 1976 to May 1977, there are a total of more than 1350 puzzles available on the site.

There are 31 puzzles remaining to post from the Puzzle series, all from 1977, which fill the gap after the final Tantalizer puzzle.

[puzzle33]

Puzzle 34: We compete. Who does what?

From New Scientist #1085, 12th January 1978 [link]

The jobs of my five employees, Alf, Bert, Charlie, Duggie and Ernie, have been changing rather frequently lately and I am afraid that I have got slightly out of touch. It was rather important for me, however, to find out who does what, as they had recently been having a test designed to find out more about their assorted capabilities and it was clearly important for the Managing Director to know just what had been happening in the past so that he could predict the future.

The information that I managed to get about their jobs and their places in the test (in which there were no ties) was as follows:

1. Bert was as many placed below the Worker as he was above the Door-Knob-Polisher.

2. The Door-Opener was three places above Charlie.

3. Alf’s place was even and the Door-Shutter’s place was odd.

4. The Bottle-Washer was two places above Ernie.

In what order did they come in the test, and what were their jobs?

[puzzle34]

Puzzle 35: Letters for digits — a multiplication

From New Scientist #1086, 19th January 1978 [link]

In the multiplication sum below the digits have been replaced by letters. The same letter stands for the same digit whenever it appears, and different letters stand for different digits.

Write the sum out with letters replaced by digits.

[puzzle35]

Puzzle 36: Football (4 teams: old method)

From New Scientist #1087, 26th January 1978 [link]

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

(2 points are given for a win and 1 point for a draw).

Find the score in each match.

A correction was published with Puzzle 39, as follows:

In the solution to Puzzle 36, the table should have shown that D played one match. The error is regretted.

I have made this change in the table above.

[puzzle36]

Puzzle 37: The bumbling B

 From New Scientist #1088, 2nd February 1978 [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 Shilli Shallas who make statements which are alternately true and false, or false and true.

This story deals with three inhabitants of the island, one from each tribe, whom we shall call AB and CA and C each make a statement, but B, who goes through life in a bumbling and idle sort of way, does not in fact say anything on this occasion, although of course when he does speak he conforms to the strict rules of his tribe.

A and C‘s statements are as following:

A: B is not a Wotta Woppa;
C: If I were to ask B what tribe A belonged to, he would, quite rightly, say Shilla Shalla.

To which tribes to AB and C belong?

[puzzle37]

Puzzle 38: Division — some missing figures

 From New Scientist #1089, 9th February 1978 [link]

A division sum — find the missing digits.

[puzzle38]

Puzzle 39: One letter wrong

 From New Scientist #1090, 16th February 1978 [link]

In the addition sum below with letters substituted for digits all is not, I fear, as it should be. Each letter ought to stand for the same digit wherever it appears and different letters ought to stand for different digits; but Uncle Bungle has once more failed us and there is one mistake (that is to say, one of the letters is wrong on one of the occasions on which it appears — if it appears more than once).

Find the mistake. Write out the correct addition sum.

[puzzle39]

Puzzle 40: The washing machine that didn’t

 From New Scientist #1091, 23rd February 1978 [link]

“A detective is what I am, my dear Sergeant Simple”, as Professor Knowall has so often said to me.

“And detection is what I am interested in, even though the facts and objects to which you call my attention may appear to be only trivial and unimportant pawns in the game of life”.

When the mystery of the washing machine, therefore, was brought to my notice it seemed reasonable to take the professor at his word and put the facts before him.

This machine, I’m afraid, was not the washing machine it had been. Errors, inefficiencies and failure to wash had somehow crept in. I did not feel, however, that I could reveal the terrible things that this machine had been doing and I therefore decided that a screen of anonymity was required.

And so neatly anonymous did I make it that the results looked like this:

1. D, E is followed by q, r;
2. B, C, E is followed by q, s, t;
3. A, C, D is followed by p, t.

I showed this proudly to the professor, but I am afraid that his reaction was disappointing.

“Can’t you ever get things right, Sergeant?”, he said.

It is a humble Simple who has to confess to his public that the professor was once more quite right. There was one mistake in the causes, i.e., in the capital letters, so that to get it right one either has to cross one out or add another one (say, F).

On the assumption that each of the faults are caused by single events and not by two or more in conjunction or separately, what can you say about Sergeant Simple’s mistake and about the causes of the various defects?

[puzzle40]

Puzzle 41: Division

 From New Scientist #1092, 2nd March 1978 [link]

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

Rewrite the sum with the letters replaced by digits.

[puzzle41]

Puzzle 42: Football – four teams

 From New Scientist #1093, 9th March 1978 [link]

Four football teams are to play each other once. After some of the matches had been played a table was drawn up giving some details of the matches played, won, lost, etc. But unfortunately Uncle Bungle had been at it again and the digits (from 0 to 9) had been replaced by letters. Each letter stood for the same digit wherever it appears and different letters stood for different digits.

The table looked like this:

(Two points are given for a win, and one point to each side in a drawn match).

Find the score in each match.

[puzzle42]

Puzzle 43: Addition

 From New Scientist #1094, 16th March 1978 [link]

Below is an addition sum with letters substituted for digits. The same letter stands for the same digit wherever it appears, and different letters stand for different digits:

Write the sum out with numbers substituted for digits.

[puzzle43]

Puzzle 44: Men-only Mews

 From New Scientist #1095, 23rd March 1978 [link]

At the time with which this story deals Alf, Bert, Charlie, Duggie and Ernie were living in separate houses in Men-only Mews.

It is useful for the managing director to know the address of his staff, but I’m afraid this information was not very easy to obtain.

However, I did manage to get some of them to tell me something:

Duggie said that the number of his house was three times the number of Bert’s.

Alf said that his number was odd, and was 23 more than Ernie’s.

Bert said that his number was nine less than Alf’s.

And Charlie said that his number was halfway between Bert’s and Duggie’s.

Men-only Mews has houses numbered from 1-50.

Find the numbers of all their houses.

[puzzle44]

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