# Enigmatic Code

Programming Enigma Puzzles

## Puzzle #214: Seven up!

My burglar alarm won’t stop beeping. I need to enter the four-digit code, but I just can’t remember what it is.

I do remember that I chose a number that is divisible by 7. I also know that I chose a number in the thousands. I recall that the numbers formed by the first three digits and the last three are divisible by 7 as well. I also deliberately chose four different digits. Finally, I know that if I add all the digits, their sum isn’t divisible by 7, but if I add add the digits of that sum, the result is divisible by 7.

Can you help me work out what my code is to stop the incessant beeping?

[puzzle#214]

## Tantalizer 3: Café de Gaulle

From New Scientist #555, 6th July 1967 [link]

My friend Jones has food poisoning, which serves him right. Last night he thought he would impress two girls by taking them to dinner at the newly opened Café de Gaulle. Since the girls have survived the ordeal, we may assume that the trouble lay in a dish which Jones ate and they did not.

Potage Tiede … 1s
Haricots sur Toast … 2s
Coctaile de Crevettes … 3s

Bulle et Couic … 4s
Crapeau dans le Trou … 5s
Trotteurs de Cochon … 6s

Fromage Souriciere … 2s
Morceau Singulier Gallois … 3s
Becasse Ecossaise … 4s

Jones tells me that each of them ate one item from each course and that, not counting tips etc., he paid eight shillings for himself, nine shillings for Polly and 10s for Gladys. No dish eaten by Polly was also eaten by Gladys.

He was in fact able to recall what the girls had eaten and so even though he had forgotten what he ate himself, we could deduce what had poisoned him. The offending dish can, however, be deduced merely from the information given so far plus the information that someone had Becasse Ecossaise.

Which is it?

In the book Tantalizers (1970) a reworded version of this puzzle appears under the title: “Café des Gourmets”.

[tantalizer3]

## Enigma 829: How do you manage without one?

My word processor has developed a fault. There’s one particular digit which it will not type: if you press the appropriate key absolutely nothing happens.

I can, for example, type the cube of 4 correctly, but not the square. Whereas for the larger number 78 (whose number of digits is less than the one-figure number I cannot type) I can correctly type both its cube and square.

Which digit do I keep missing out?

#### News

Between the Enigmatic Code and S2T2 sites there are now 3000 puzzles available.

On Enigmatic Code there are now 1658 Enigma puzzles available (which leaves 134 remaining to post). All 90 puzzles from the Puzzle series are available, as well as 215 from the Tantalizer series (and about 283 that are not yet posted). And we have all puzzles from the current Puzzle # series (which is ongoing, and most recently reached Puzzle #213).

And on the S2T2 site there are currently 840 Teaser puzzles available (these are also ongoing, and has just reached Teaser 3156, so there are quite a lot of those remaining. But I have been working through the published books of puzzles and newspaper archives that are available).

Along with a few additional puzzles that brings the total to the magical 3000.

If you have been playing along with me and have solved all the puzzles posted so far, then well done! It has been quite a journey.

As long as I have the time I will keep posting puzzles to the sites. Thanks to those who have contributed to the site, either by sourcing puzzles or sharing their solutions.

Happy Puzzling,

— Jim

[enigma829]

## Puzzle #213: Cross sward

Older age does bring some benefits. My daughters Kate and Laura have offered to help me by taking on the maintenance of my garden, which is rectangular with a small, rectangular vegetable plot in one corner. The remainder is lawn.

To make it fair for them, I have agreed that my last job in the garden will be to partition it into two with a straight fence, with each daughter getting the same area.

Kate suggested that we forget about the vegetable plot, and only divide the lawn. She sketched a line on the diagram that would give them each exactly half the lawn (with no awkward pinch point to get the mower through). Laura, meanwhile, drew a fence that would divide the lawn and the vegetable patch into halves. To make their lines, neither daughter needed to measure anything, they just needed a straight edge.

Can you draw the lines on which Kate and Laura propose to build fences?

[puzzle#213]

## Tantalizer 2: A chess puzzle

From New Scientist #551, 29th June 1967 [link]

Frank French, our local chess secretary, was writing out the results of our all-against-all tournament, when in popped Barbara Bocardo, the well-known logician.

“What gives?”, she asked, pouncing on the score sheet, which looked like this:

“The half points are draws”, he explained. “I’ve filled in all there were and next I shall record the 1’s (wins) and 0’s (losses)”.

“Don’t do that. Let me guess. How did you do yourself?”

“Well, I drew in four of the five rounds, as you see. But alas, I finally shared bottom place with Alapin, my opponent in the first round.”

“A lot of draws, surely?”

“Yes. At least one in every round. Each of us drew in at least two consecutive rounds.”

“Did the winners (I see there must have been two of them), meet in the second round?”

“No”.

“Good. It is now possible to deduce whom they played in the last round.”

Can you perform this logical feat?

[tantalizer2]

## Enigma 814: Mixed and matched

I had a day at the health club recently. I planned to have one full session of squash, one full session of badminton and one full session in the sauna (but not necessarily in that order) with at least a one-hour break between each of the sessions. The club’s timetable of sessions is shown above.

By coincidence my colleagues Mark and Jenny also spent the day there with the same idea in mind (although none of us necessarily did any of the activities together).

Our boss (who knew all the above facts) tried to telephone me at one stage but was told I was busy. From this he was able to work out my exact day’s schedule.

An hour later he tried to telephone Mark but was told he was busy and he was told the activity which Mark was engaged in. From this my boss was able to work out Mark’s exact schedule.

Another hour later he tried to telephone Jenny but was told she was busy and he was told the activity which Jenny was engaged in. From this my boss was able to work out Jenny’s exact schedule.

Which is the correct order of the men’s, women’s, and mixed sessions in the sauna?

[enigma814]

## Puzzle #212: Sound off

“Why isn’t the sound working?”, Mum muttered as she hit the mute key on the remote control.

“You’ve probably got the wrong remote, Mum”, Sam said. “Remember, it’s the long, thin one for the television, the wide one for the set-top box and the little one for the speakers. Which one did you mute?”

“I can’t remember”, said Mum, as she got her thinking cap on to try to fix things.

To get sound, all three remotes have to be unmuted. Mum came up with the most efficient system for cycling through the possible combinations of muting and unmuting, and got to work.

What is the maximum number of presses needed if she wanted to be sure of getting the sound back?

[puzzle#212]

## Tantalizer 1: Publish or perish

From New Scientist #550, 22nd June 1967 [link]

Kappa, Lambda, Mu and Omicron are at present uneasily seated in the Warden’s study at Jude’s College, awaiting summonses from the committee which will appoint one of them to the vacant Fellowship in Greek Literature. Each is hugging his only published work and each suspects that the post will go to the author of the longest, irrespective of all possible merit.

From their stilted but cunning conversation, the following facts have so far emerged:

Each book has a whole number of pages over 100.

Only Lambda’s book and Mu’s book have the same number of pages.

The total number of pages in all four books is 500.

Mu then asked Omicron whether the number of his (Omicron’s) pages was a perfect square. From Omicron’s answer Mu and Kappa made silent and independent deductions with impeccable logic. Mu deduced that Omicron’s book was the longest. And Kappa, who was not a perfect square, deduced that Omicron’s answer was not the truth.

How many pages are there in each man’s book?

This was the first Tantalizer puzzle published in New Scientist. It was accompanied by the following introduction:

This is the first of a series of logical puzzles compiled by Martin Hollis. No mathematical knowledge is required for their solution. A new puzzle will appear each week, and the answer will be printed in the following week’s issue.

[tantalizer1]

## Enigma 813: Easy as ABC

The schedule of matches has been drawn up for the next tournament between Albion, Borough, City, Rangers and United, in which each team will play each of the other teams once. Two matches will take place on each of five successive Saturdays, each of the five teams having one Saturday without a match.

Two of the five teams will be meeting their four opponents in alphabetical order. Given this information you could deduce the complete schedule of matches if I told you either one of the matches scheduled for the first Saturday.

1. Which teams will be meeting their opponents in alphabetical order?

2. Which matches are scheduled for the first Saturday?

[enigma813]

## Puzzle #211: Cross purposes

Debbie and Hoi are playing a game where they take turns to cross out numbers written on a piece of paper.

Each player must cross out a divisor or a multiple of the number most recently crossed out. The first player who is unable to cross out a number loses.

Hoi goes first and crosses out 11. Debbie smiles, knowing she can now win in three moves. What number does she cross out?

[puzzle#211]

## Tantalizer 313: La Dolce Vita

Seven couples rented a villa for the week in Majorca. They arrived on a Monday and dived beneath the sheets. They didn’t see much of the ocean but devoted a fabulous week to musical beds instead.

Partners were changed daily. Angela, for instance, spent Monday with Tommy, Tuesday with Upton, Wednesday with Vaughan, and Thursday with William.

Barbara kicked off with Xerxes followed by Yvan, Upton, and Zeno in that order. Cutie partnered with Tommy on Wednesday, Xerxes on Thursday, and William on Friday.

Delia spent Monday with Vaughan, Wednesday with William, Friday with Xerxes, and Saturday with Yvan. Yvan devoted Thursday to Esther and Monday to Fiona, whose partner on Thursday was Upton. Esther and Xerxes spent Saturday together, as did Fiona and Tommy. Esther and William made their whoopee on Monday.

These facts are kindly supplied by Gillian, who adds demurely that Sunday’s pairs were all decently married to one another. This was not only proper but also necessary for all possible mixed pairs to have had a day’s delight by the end of the holiday.

Who is married to whom?

[tantalizer313]

## Enigma 812: Upon my word!

I once had a job in a department store, working in the House Name Department. For example, I had to make “Dunromin” (taking 8 letters) and “Four hundred and twenty-one” (taking 23 letters).

On one occasion a customer ordered his three-figure house number spelt out in this way. I prepared the invoice and wrote on it (in figures) the number of letters used. But the invoice clerk thought this referred to the house number so he replaced it (in figures) with the number of letters that house number would take.

His superior again thought the number referred to the house number so he replaced it (in figures) with the number of letters that house number would take.

The auditor again thought the number referred to the house number so he replaced it (in figures) with the number of letters that house number would take. He then prepared the bill accordingly. The customer turned out to be very lucky: at each stage in this long process the number had been reduced and the bill was for less than half what the Es alone would have cost.

How many letters should the customer have been charged for?

[enigma812]

## Puzzle #210: Action station

I have a train to catch! I was planning to drive or cycle to the station, but, to my dismay, I realise that my car has a flat battery and my bike has a puncture.

I look at the clock and realise that, based on past experience, if I were to set out right now and walk to the station, I would miss my train by 10 minutes. However, if I were to run at my top speed, I would be 15 minutes early. It is freezing outside and I don’t fancy waiting on the platform for any longer than I have to.

It is too late to do any more calculations as I need to leave right now. I decide to run for half the distance and walk the rest of the way. But where are my running shoes? After a frantic search, I find them.

I leave the house 2 minutes later. Do I make it in time to catch the train?

[puzzle#210]

## Enigma 811: To change or not to …

Uncle Delroy had £3 for each of his nephews Sam and Tom and his niece Anna. For each child Uncle Delroy changed the money into 300 pence. He gave them 300 tests and they got a penny for each test they succeeded at.

Each test involved three boxes labelled 1, 2 and 3. While the child was not looking Uncle put a coin in one of the boxes. The child then chose one of the boxes. Uncle then chose one of the two other boxes; he always chose an empty box. He opened it and showed it was empty to the child. He then asked the child if he or she wished to change their choice to the other unopened box. After the child has either changed boxes or stayed with their original choice, they opened their final choice of box; if it contained the coin then they kept it otherwise the coin went to Uncle Delroy’s favourite charity.

Sam reckoned that Uncle showing him an empty box was no help so he never changed his choice. On the other hand Anna reckoned that uncle showing her an empty box did tell her something so she always changed her choice. Tom did not change in his first test but, for every other test, he changed if and only if he had lost in the previous test.

After the tests the following facts emerged. They each made a correct initial choice in the same number of tests. Tom lost in his first test, won in his last test and never won in two consecutive tests. Uncle paid out a total of £4.

How much did each child get?

[enigma811]

## Puzzle #209: Postman’s knock

There was a knock at Professor Numero’s door. It was a postal worker.

“Excuse me disturbing you, but can you help? This letter has a cryptic address. I can’t make head or tail of it:”

To the Resident,
The house with a number whose digits when multiplied together give five times what they sum to, Long Road.

The professor pondered. “Well, you’ve come to the right road. And, luckily, there’s only one house number in the road with this mathematical property — the one at the end, where Colonel Crypto lives”.

As you would expect, the houses in Long Road are numbered consecutively from 1 upwards, with no missing numbers.

How many houses are there in the road?

[puzzle#209]

## Enigma 809: What’s the score?

From New Scientist #1964, 11th February 1995 [link]

In rugby union a try is worth 7 points if converted or 5 points if unconverted; a penalty goal or drop goal is worth 3 points. There are no other forms of scoring.

1. If in a match the winning side’s score is such that they cannot have scored any unconverted tries and the losing side’s score is such that they must have scored a converted try, what is each side’s score?

2. If in a match the winning side’s score is such that you know the number of tries that they scored and the losing side’s score is such that you cannot be sure of the number of tries that they scored, what is each side’s score?

3. If in a match the winning side’s score is such that they must have scored at least one penalty goal or drop goal and the losing side’s score is such that even if I tell you their score and the number of tries that they scored it is possible that you still cannot be sure how many of those tries were converted, what is each side’s score?

[enigma809]

## Puzzle #208: Flower power

Ivor Plant is the head gardener of Lady Bird’s estate. Her large chrysanthemum garden needs to be weeded and pruned, so he assigns his two apprentices, Lupin and Heath, to the rather tedious task. The garden consists of a central 4-metre-sided square (pink) inscribed in a circle, and four outer areas (blue) enclosed in semicircles that are connected to the square’s corners.

“If you give me two of your chocolate biscuits, I will let you pick whichever area you want to weed: the outside or the inside”, says Heath to Lupin. Always eager to get out of extra work whenever possible, Lupin agrees.

If he is looking to weed the smaller of the two areas, should he choose the blue or the pink section?

[puzzle#208]

From New Scientist #863, 13th September 1973 [link]

Old George was recalling the long defunct West Wessex Railway in the snug at the Railway Arms the other night. There were nine stations – Axle, Bundle, Cordwain, Dawdle, Egdon, Foxfair, Gudgeon, Hangover and Inkwell – all exactly one mile apart in alphabetical order in a straight line.

George was the ticket inspector and took his duties seriously. He used to board the early train at Hangover and thereafter alight at a station every so often and wait for another train from there. It was a long, grimy day, since, of each pair of stations more than two miles apart, he boarded a train at one and got off it at the other. Each of these pairs, however, were only so used once during the day and only in one direction. Nevertheless he was glad to step out of the final station and into the snug of the Railway Arms.

Where is the Railway Arms?

[tantalizer312]

## Enigma 810: Wooded acres

Having a few moments to spare one Thursday, I decided to measure the dining table. This is a fairly conventional piece of furniture in dark oak, rectangular in shape, the longer side less than double the width.

It emerged that whether the surface area is expressed in square yards, square decimetres, square feet, hectares or square light-years, the first significant digit is the same. Furthermore, whether the length of the table is expressed in yards, miles, millimetres or light-hours, the first significant digit is again the same one, and this applies also to the length of the diagonal.

The length of the perimeter is an exact whole number of half-inches, the area in square centimetres is an integral number which is a perfect cube, and the speed of light in my dining room is 0.3 kilometres per microsecond.

Please ascertain the width of the table in feet, to four significant figures.

[enigma810]