Enigmatic Code

Programming Enigma Puzzles

Category Archives: puzzle

Puzzle 63: One and one make two

From New Scientist #1114, 3rd August 1978 [link]

“Never tell them more than you need”, as Professor Knowall has so often said. “And pay them the compliment, my dear Sergeant Simple, of supposing that they are capable of putting one and one together to make two”.

As my readers will know, the professor, though he does not often have the time to turn his attention to anything other than crime, is very interested in football and likes making up and solving football puzzles. His remarks about putting one and one together to make two seemed rather silly to me at first, but I soon realised what he meant when he showed me the puzzle.

It was about four football teams, and gave some information concerning the number of matches played, won, lost and so on. But of the 24 pieces of information that one might have expected only 12 were given. One did indeed need to put one and one together to make two.

The information was as follows:

“That ought not to be too hard for you, my dear Sergeant”, he said, “but I must add also the information that not more than seven goals were scored in any match”.

I’m afraid it was too much for me, but I hope that the readers will be able to find out the score in each match.

(Each team is eventually going to play each other once).

[puzzle63]

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Puzzle 64: Addition: digits all wrong

From New Scientist #1115, 10th August 1978 [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.

Find the correct addition sum.

[puzzle64]

Puzzle 65: Division: figures all wrong

From New Scientist #1116, 17th August 1978 [link]

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

The correct division, of course, comes out exactly. All the digits in the answer are only 1 out, but all the other digits may be incorrect by any amount.

Find the correct figures.

[puzzle65]

Puzzle 66: Hopes and successes on the island

From New Scientist #1117, 24th August 1978 [link]

I had been away from the Island of Imperfection for some time and I was amused — and rather distressed — on a recent visit to find that there was now another tribe there.

But I had better explain. In the old carefree days, which I knew so well, there had been three tribes on the island. The Pukkas, who always told the truth, the Wotta-Woppas, who never told the truth, and the Shilla-Shallas, who made statements which were alternately true and false or false and true. I cannot pretend to know how it happened but now there is another tribe who call themselves the Jokers. I am afraid that all I can tell you about them is that in making three statements their truth-telling rules are any rules that are different from those of the other three tribes. Just to be different! That seems to be all they are interested in, and I find it hard to restrain myself from making some acid comments about the modern generation. They don’t seem to be much interested in fun or laughter but in achievement. And it is no doubt because of this that the main currency of the island is called a Success, and it made up of 100 Hopes.

Four men, ABC and D (one from each tribe), make statements as follows:

A: (1) B makes more true statements than D does.
A: (2) My income is 7 Successes and 50 Hopes per week more or less than D‘s income.
A: (3) C is a Wotta-Woppa.

B: (1) A‘s income is 2 Successes and 50 Hopes per week more or less than mine.
B: (2) D‘s second statement is true.
B: (3) C‘s income is 8 Successes and 50 Hopes per week.

C: (1) D is a Joker.
C: (2) My income is 10 Successes per week.
C: (3) B is a Pukka.

D: (1) B is a Joker.
D: (2) My income is 1 Success per week more or less than C‘s income.
D: (3) C is not a Joker.

It was rather interesting to notice that the more truthful a man the less was his income. All their incomes were a multiple of 50 Hopes.

Find the tribes to which ABC and D belong and their weekly incomes.

[puzzle66]

Puzzle 67: Addition: letters for digits

From New Scientist #1118, 31st August 1978 [link]

It is, I admit, a moot point whether it is better to guess at some of Uncle Bungle’s illegible letters and to hope for the best, or just to leave them out. For some time now I have guessed, but I must admit that my guessing is not what it was, so in this sum anything that is illegible has just been left out. Letters stand for digits, and the same letter stands for the same digit whenever it appears, and different letters stand for different digits. In the final sum all the digits from 0-9 are included.

Write out the correct addition sum.

[puzzle67]

Puzzle 68: Football and addition: letters for digits

From New Scientist #1119, 7th September 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. The three 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 scores in the football matches and write out the addition sum with numbers substituted for letters.

[puzzle68]

Puzzle 69: Division: letters for digits

From New Scientist #1120, 14th September 1978 [link]

For some reason Uncle Bungle does not like divisors. This has been left out in the latest division sum which he has produced with letters substituted for digits. Here it is:

Find the divisor and all the digits of the sum.

[puzzle69]

Puzzle 70: Football five teams: new method

From New Scientist #1121, 21st September 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. Once can get some idea of the success of the method from the fact that in the latest competition between 5 teams, when some of the matches had been played, each team had scored at least 1 goal in every match. They are eventually going to play each other once.

The points were as follows:

A   11
B    8
C   12
D    5
E   43

Not more than 9 goals were scored in any match.

What was the score in each match?

[puzzle70]

Puzzle 71: All wrong, all wrong

From New Scientist #1122, 28th September 1978 [link]

A couple of one’s, a couple of two’s and a six;
All wrong, all wrong!

If only I thought that the puzzle was one I could fix,
I’d sing a song.

But as I feel sure that it’s rather too much for me,
My voice is muted.

Uncle Bungle’s my name and I fear that you must agree,
I’m rather stupid.

So please, I implore,
Continue the fight,
With tooth and with claw,
With main and with might,
To make wrong sums right.

puzzle-71

The figures given are all incorrect. Write out the whole division sum.

[puzzle71]

Puzzle 72: Addition: letters for digits

From New Scientist #1123, 5th October 1978 [link]

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

Write the sum out with numbers substituted for letters.

[puzzle72]

Puzzle 73: A division sum. Find the missing digits

From New Scientist #1124, 12th October 1978 [link]

puzzle-73

[puzzle73]

Puzzle 74: Football (three teams, old method)

From New Scientist #1125, 19th October 1978 [link]

Three football teams (AB and C) are to play each other once. After some — or perhaps all — the matches had been played, a table giving some details of goals, and so on, looked like this:

puzzle-74

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

Find the score in each match.

[puzzle74]

Puzzle 75: C is silent

From New Scientist #1126, 26th October 1978 [link]

The four tribes seem now, for better or worse, to be firmly established on the Island of Imperfection. They are the Pukkas, who always tell the truth; the Wotta-Woppas, who never tell the truth; the Shilla-Shallas, who make statements which are alternately true and false or false and true; and the Jokers, whose rules for truth-telling in making three statements are any rules that are different from those of any of the other three tribes.

In the story which I have to tell about ABC and D there is one member of each tribe. C, I am afraid, does not actually say anything. Can he just be fed-up? I don’t blame him. The other three speak as follows:

A: B is a Pukka;
B: C is a Shilla-Shalla;
D: A is a Pukka;
D: I am a Shilla-Shalla or a Wotta-Woppa;
D: B is a Joker.

Find the tribes to which ABC and D belong.

[puzzle75]

Puzzle 76: Addition: letters for digits (one letter wrong)

From New Scientist #1127, 2nd November 1978 [link]

Below is an addition sum with letters substituted for digits. The same letter should stand for the same digit wherever it appears, and different letters should stand for different digits. Unfortunately, however, there has been a mistake and in the third line across one of the letters is incorrect. The sum looks like this:

Which letter was wrong? What should it be? Write out the correct addition sum.

[puzzle76]

Puzzle 77: Letters for digits: a multiplication

From New Scientist #1128, 9th November 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.

[puzzle77]

Puzzle 78: Football: new method

From New Scientist #1129, 16th November 1978 [link]

Three teams, AB and C are all to play each other once at football. 10 points are given for a win, 5 points for a draw and 1 point for each goal scored whatever the result of the match. After some, or perhaps all, the matches have been played the points were as follows:

A   21
B   20
C    4

Not more than 6 goals were scored in any match.

What was the score in each match?

[puzzle78]

Puzzle 79: Division: some letters for digits, some digits missing

From New Scientist #1130, 23rd November 1978 [link]

In the following division sum most of the digits are missing, but some are replaced by letters. The same letters stand for the same digit whenever it appears:puzzle-79

Find the correct sum.

[puzzle79]

Puzzle 80: Addition: letters for digits

From New Scientist #1131, 30th November 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:

puzzle-80

Write the sum out with numbers substituted for letters.

[puzzle80]

Puzzle 81: Uncle Bungle and the vertical tear

From New Scientist #1132, 7th December 1978 [link]

It was, I’m afraid, typical of Uncle Bungle that he should have torn up the sheet of paper which gave particulars of the numbers of matches played, won, lost, drawn and so on of four local football teams who were eventually going to play each other once. Not only had he torn it up, but he had also thrown away more than half of it onto, I suspect, the fire, which seems to burn eternally in Uncle Bungle’s grate. The tear was a vertical one and the only things that were left were the “goals against” and the “points” — or rather most of the points, for those of the fourth team had also been torn off.

What was left was as follows:

puzzle-81

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

It will not surprise those who know my uncle to hear that one of the figures was wrong, but fortunately it was only one out (i.e. one more or one less than the correct figure).

Each side played at least one game, and not more than seven goals were scored in any match.

Calling the teams ABC and D in that order, find the score in each match.

[puzzle81]

Puzzle 82: A cross number

From New Scientist #1133, 14th December 1978 [link]

puzzle-82

(There are no 0’s).

Across:

1. Each digit is odd and is greater than the one before.
4. The digits are all different and this is a multiple of the number which is 3 greater than 1 down. Even when reversed.
5. A perfect cube.

Down:

1. 17 goes into this.
2. A multiple of 1 down.
3. Each digit is odd and is less than the one before.

One clue is incorrect. Which one?

With which digit should each square be filled?

[puzzle82]