Enigmatic Code

Programming Enigma Puzzles

Category Archives: puzzle

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In the multiplication sum below the digits have been replaced by letters.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]

Puzzle 45: Football

 From New Scientist #1096, 30th March 1978 [link]

The new method of rewarding goals scored in football matches goes from strength to strength. In this method 10 points are given for a win, 5 points for a draw and 1 point for each goal scored. One can get some idea of the success of the method from the fact that in the latest competition between teams, when some of the matches had been played each team has scored at least one goal in every match.

The points were as follows:

A      11
B       8
C      12
D       5
E      42

Not more than nine goals were scored in any match.

What was the score in each match?

[puzzle45]

Puzzle 46: I lose my specs

 From New Scientist #1097, 6th April 1978 [link]

In the division sum below letters stand for different digits. But unfortunately I did not have my specs with me when I copied it out and discovered later that I had made a mistake. One letter was wrong on one of the occasions when it appeared.

Find the incorrect letter, and rewrite the sum with the letters replaced by digits.

[puzzle46]

Puzzle 48: Verse on the island

From New Scientist #1099, 20th April 1978 [link]

We live, we three, on the Imperfect Isle,
Where all is not just what it ought to be.
One is a Wotta-Woppa and he never
Tells what is true, in fact a liar he.

And then there is another one who cannot
Make up his mind. Oh, shall I tell a lie?
He is a Shilli-Shalla, and makes statements,
One true, one false. But which? The constant cry.
The third one is a Pukka and we find
Nothing but truth comes from the third man’s mind.

Single figures all our dwellings,
And each one is different.
Three statements each, so read with care
And use your loaf to find what’s meant.

A:

(1) First let me say no Shilli-Shalla I,
But I’m afraid I cannot tell you why!
(2) Then I point out that where numbers are concerned
The lower the truer; that’s the fact for which you yearned.
(3) Thirdly, no tricks,
My number’s less than six.

B:

(1) and (2) A Pukka, I, and live at number one.
That’s two statements in a single line.
(3) Perfect, you might say, but not as perfect as C‘s square.

C:

(1) A and B live on either side of me.
(2) Who is the Wotta-Woppa? Why it’s B.
(3) And now our verse
Has done its worst.
Just to finish with a wink,
To get this right you’ll have to think.
And with a nod,
A‘s number is not odd.

Where do AB and C live and what are their tribes?

[puzzle48]

Puzzle 47: Digits all wrong

From New Scientist #1098, 13th April 1978 [link]

In the following addition all the digits are 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.

Find the correct addition sum.

[puzzle47]

Puzzle 49: Division

From New Scientist #1100, 27th April 1978 [link]

In the following long division sum, some of the letters are missing and some of them are replaced by letters. The same letter stands for the same digit whenever it appears and different letters stand for different digits:

Write out the complete division sum.

[puzzle49]

Puzzle 50: Football and addition

From New Scientist #1101, 4th May 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 whenever it appears and different letters stand for different digits. The 3 teams are eventually going to play each other once — or perhaps they have already done so.

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

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

[puzzle50]

Puzzle 51: A multiplication

From New Scientist #1102, 11th May 1978 [link]

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

You are told that A is not greater than 5.

Find the digits for which the letters stand.

[puzzle51]

Puzzle 52: Football on the Island of Imperfection

From New Scientist #1103, 18th May 1978 [link]

There has been a great craze for football recently on the Island of Imperfection and I have been fortunate enough to get some details of games played there.

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.

Three teams, one from each tribe, have been having a competition, in which eventually they will play each other [once] — or perhaps they have already done this. The secretaries of the three teams have been asked to give details of the number of matches played, won, lost and drawn and they do this in accordance with the rules of their tribe — so that, for example, all the figures given by the secretary of the Wotta-Woppa team will be wrong.

The figures given are as follows (calling the teams AB and C in no particular order):

(In no instance did a team win by a majority of more than three goals).

Find the tribe to which each of the three teams belong, and the score in each match.

[puzzle52]

Puzzle 53: Addition

From New Scientist #1104, 25th May 1978 [link]

In the following addition sum the digits have been replaced by letters. The same letter stands for the same digit wherever it appears and different letters stand for different digits.

Find the digits for which the letters stand.

[puzzle53]