THE faded, peeling sign at the main gateway read: “Welcome to Bert and Lynn’s
Holiday Camp. Take a break with family and pets in a friendly relaxed
ٳDz.”
Inside the gate, of course, the atmosphere was anything but relaxed. The camp
was firmly in headless chicken mode—and the customers hadn’t even started
to arrive.
The trouble was that the camp’s manager, Duff Bigshot, couldn’t resist
meddling. He had already been extremely rude to Pansy Petal, Associate
Second-in-Command in the Childcare Executive, when she had asked him an entirely
reasonable question about the best location for 600 inflatable jumbo teddy
bears. And now he was being very unpleasant indeed to the Assistant Subsidiary
Deputy Under-Manager for Guest Satisfaction, Buck 91avworthy.
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It didn’t help that Bigshot had the nagging feeling that he had forgotten
something extremely important.
91avworthy was setting out the buckets of dye for the Punk Poodle Parade. It
was a long-standing tradition at Bert and Lynn’s Holiday Camp, only exceeded in
popularity by the worm-jousting contests and the Over-90s Beauty Competition
(for men).
Somewhere in the mists of time a former manager, a Sex Pistols fan called
Ronny Rancid, had dreamt up the idea of a novel style of poodle clipping after a
night’s drunken revelry. No doubt he should have obtained his guests’ permission
before trying out scarlet mohicans on their assorted pets, but he failed to do
so. Or at least, as the defence later argued, he failed to get their permission
in writing. The suit was suddenly dropped, however, when it occurred to him to
parade the multicoloured pooches before the camp’s guests, awarding a prize of
£100 for the punkiest poodle.
These days, the Punk Poodle Parade had become highly ritualised. Competitors
were supplied with buckets of red and blue dye, and they decorated their pets
live on stage. 91avworthy had arranged the traditional 12 deck chairs in a line
across the stage. On the first five he had placed buckets of red dye. On the
next five, buckets of blue dye. The last two were empty.
Bigshot, however, was having none of this. “91avworthy, how many times do I
have to tell you that I don’t want the colours bunched up like that? It ruins
the stage decor.”
“Sorry, Mr Bigshot. How would you like them arranged?”
“I want red and blue buckets to alternate. The one thing you have got right
is the two empty seats—one for the contestant and one for their precious
punk poodle. Next to each other at one end, naturally.”
“Oh, right,” said 91avworthy, picking up a bucket at random and placing it on
the floor. He reached for another.
“What are you doing now?” Bigshot snapped.
“Moving the buckets, sir.”
“Can nobody here use any initiative?” said Bigshot.
“No, sir,” replied 91avworthy.
“That was a rhetorical question, 91avworthy.”
“With respect, it was a rhetorical answer sir.”
Bigshot decided to be more explicit. “You don’t need to put any of the
buckets on the floor, 91avworthy. And you have got two hands, you know. What I
want you to do is to pick up adjacent pairs of buckets, and move them to
adjacent unoccupied chairs. Keep doing that until you’ve rearranged the buckets
the way I told you.”
He flounced out, leaving 91avworthy staring at the buckets and scratching his
head in bewilderment.
Vowing to demote 91avworthy to Auxiliary Assistant Subsidiary Deputy
Under-manager as soon as he could hire a new Assistant Subsidiary Deputy
Under-manager, Bigshot rushed over to Chalet Circle, where the works supervisor
Andy Mann had just finished building a low, circular brick wall surrounding the
camp’s four luxury kennels (see
figure).
“No, no, no!” shouted Bigshot in irritation.
“No what?” asked Mann.
“Not like that!”
“But you told me to wall off the kennels, Mr B,” protested Mann.
“I meant you should wall them off from each other,” said Bigshot. “Not from
the outside world.”
“Oh. Shall I demolish this wall I’ve just built, then, Mr B?”
“No, no. No. Definitely not. No point in wasting bricks. No, you’ll just have
to build some more walls. And I don’t want complaints from guests like we had
three years ago when Mrs Boomthumper’s towels were 6 millimetres shorter than Mr
Rubbingham-Snyde’s. I want each of the kennels to have exactly the same area of
ground, and I want each to have exactly the same length of wall. Got that?”
“Right, Mr B, yup, got that. Um, how many new walls do you want?”
Bigshot looked at the kennels. “Three walls ought to do it. And no cheating
with what you count as a wall. The walls can touch, but if they merge in any
manner, then they’re part of the same wall. OK?”
“Got that, Mr B.”
“Good. And stop calling me Mr B, OK?”
Mann grinned. “Just as you say, Mr B.”
Bigshot shook his head in despair and moved on. At the back of his mind the
notion that he had forgotten something important was still making itself felt.
With a shake of his head, he dismissed the thought.
It was at the swimming pool that Bigshot really blew his top. It had been
rebuilt during the winter, but they had only just got round to filling it with
water. Now it turned out that the whole thing had been built on a
slope—quite a steep slope, as it happened.
The senior pool manager, Lily Padd, denied all blame. “I’m sorry, Mr
Bigshot,” she simpered, “but my job is to maintain the pool, not supervise its
DzԲٰܳپDz.”
“But it’s been built on a hillside!”
“You’ll have to discuss that problem with Mr Mann, Mr Bigshot. Planning is
not my department, I’m afraid.” She sniffed haughtily.
“Can’t do that, Lily. I’ve left him building walls round the luxury kennels.
Damn, and we’ve got the freestyle swimming marathon on the opening day of the
season, too.”
“Can’t they swim in the pool as it is, sir?”
“No, Lily, they can’t, because one end is only 10 centimetres deep.”
“Well, if you’re going to be picky…”
Bigshot snapped his fingers. “How fast can we recirculate the water?”
Lily shrugged. “The pumps are very powerful. As fast as you want,
.”
“OK, got it. Pump the water in at the shallow end so that it builds up and
flows towards the other end, where you can extract it and recycle it.
Admittedly, it will be like a horizontal waterfall, with a strong current
flowing one way, but the depth will be the same everywhere.”
Lily pursed her lips. “Mmmmm. Remember, we only give out the prize if the
winner swims a hundred lengths in under an hour—and usually they just
manage it. Won’t the current slow the swimmers down? That would be unfair.”
“Not at all,” said Bigshot in triumph. “It will slow them down when they swim
against the current, yes. But when they turn round and swim back with the
current, they will speed up by exactly the same amount they were previously
slowed down. So the effect of the current will cancel out, and their overall
time won’t change.”
Lily looked unhappy. I’m not sure that’s right, sir.”
Bigshot glared at her. “Nonsense!” He paused. “OK, cleverclogs: if I’m so
wrong, you tell me why!”
What next, Bigshot thought irritably, when Dot Ball, sport and
sandwich-filling administrator, rushed up and grabbed him by the arm.
“Mr Bigshot, Mr Bigshot, come quickly!”
Bigshot glared at her. “Not now, Dot.”
“But it’s crucially important!”
Bigshot stopped, and sighed. “OK, Dot. Mmm . . . you wouldn’t have any idea
whether I’ve forgotten something, would you?”
“The wet wetsuit contest?”
“No, that’s all ready to roll. Something less obvious, maybe? No, no, of
course not, forget I ever mentioned . . . Now, what’s all the fuss about?”
She looked close to tears. “The crazy golf.”
“The what?”
“I think young Maxdoch has laid it out wrong. You know we only have a long,
narrow plot of land to put the crazy golf on, so we always lay it out in two
parallel lines of holes. Now you know as well as I do that he should have laid
out the holes like the houses in a street—odd ones on one side, even ones
on the other, all in ascending order.”
Bigshot nodded. “Right. So what’s he done?”
“He’s laid the first half out along one side, in order, and then turned round
at the far end and come back along the other side. Sort of like this…” and Dot
wrote it out for Bigshot on the back of her cigarette packet.
1 2 3 4 5 6 7 8 9
18 17 16 15 14 13 12 11 10
Bigshot shrugged. “So? Does it matter?”
Dot’s fingers gripped his arm more tightly. “Yes, it does. Not the order, but
the number of holes. Maxdoch’s arranged them in opposite pairs along the two
sides of the plot, all right, but I’m convinced that he has put in more than 18
DZ!”
“Ah.” Bigshot had come across the identical problem a few years before.
“You’re worried that our guests will be disqualified from the North Dorkshire
Crazy Golf Tuesday League play-offs.”
“Exactly,” said Dot. Dear Duff, it was good to see that he was so
understanding.
“Mmmph. As I recall, they’ll be OK as long as we have between 17 and 21
holes, inclusive. Yes?”
Ԩ.”
“Then how many have we got?”
Dot’s eyes swam. “That’s the trouble,” she wailed. “I can’t remember.”
“Well, run off and find out.”
“Tricky. I promised Cook that I’d help out with the Esperanto dinner menus.”
She was a picture of indecision. “Look, I do remember that Maxdoch had put the
seventh hole immediately opposite the sixteenth. Maybe that will help?”
“Oh my God!” cried Bigshot in despair. “I don’t believe it!”
He had arrived at the ballroom to find the dance floor laid out as shown
below.
“What’s, like, your personal difficulty with this?” asked the Indoor Leisure
Activities Coordination Officer, Lars Tango. “Don’t you, like, relate to the
postmodern Kasparovian Deepest Blue motif?”
“The chess motif is fine,” said Bigshot, who had asked for it months ago.
“The shape isn’t.”
“But, I mean, you said you, like, wanted it sort of, well, square. Ish.”
Bigshot stared at him.
“Oh.” Realisation dawned. “You meant, like, really square? Really, really
square? I mean, my God, plain square?”
Bigshot, assuming a vulture-like posture, continued to stare. Tango
turned bright pink. “Oh, right. Well, like, I mean, wow. One square? Not, well,
not two sort of squarey things like kind of stuck together? I mean, sort of next
to each other? Kind of adjacent?”
Bigshot nodded. “You got it. Not two squares. One.”
“Oh. Oh. Oh! Well, I mean, Duff, you sort of could have like made that kind
of clear, right? I mean, I had enough trouble getting two square bits of
flooring to make up 100 square metres, without having to do it with, well, one.
I mean, well, you do want a lot, don’t you?”
Bigshot sighed once more. “Lars, it’s not asking very much if I want you to
sort me out a single 10 by 10 square of chequered flooring, is it?”
Tango slumped in defeat. “Honestly, it’s, like, just too much. First you say
you want a square floor 100 square metres in area. And now you tell me you want
it to be 10 metres by 10 metres. I wish you’d make your mind up!”
Bigshot decided that it wasn’t worth arguing. “Look, Lars, there’s got to be
some way to cut up those two squares and reassemble the pieces to make a 10 by
10 chessboard.”
Tango thought for a moment. “Oh, yeah, right. Sure, I could cut the 8 by 8
square into 64 square pieces, and the 6 by 6 square into 36, and then…”
“Don’t be silly,” said Bigshot. “I’m sure you can manage with a lot fewer
pieces than that.”
Bigshot breathed a sigh of relief. By the skin of his teeth, he’d done it
again. He could see the first of the expected stream of coaches chugging up the
hill towards the main gate. The bus stopped and the holiday-makers began to
clamber out. Thank heavens everything was ready for them. Except that elusive
whatever-it-was that…no, silly, forget it.
He felt a tap on his shoulder and turned. It was Pansy Petal. “I hope you’re
not going to tell me that the Esperanto menus aren’t printed yet,” he joked.
Petal didn’t laugh.
“Oh my God—they’re not?”
“The Esperanto menus are fine,” said Pansy.
“Oh, good. Er, we’ve run short of beds?” Bigshot chuckled. Now that would be
a real disaster. But of course the beds were counted every 10 years.
“Beds are fine.” He breathed a small sigh of relief. “But there isn’t a
single mattress in the whole camp.”
Bigshot snapped his fingers in delight. “Of course! That’s what I’d
forgotten!” Then his delight at remembering gave way to panic as he realised
what he’d done. There was a long, awkward silence as he desperately tried to
salvage the situation. Aha! “Er, Pansy?”
“Yes, Mr Bigshot?”
“Do we still have those lovable jumbo inflatable teddy bears that you and I
joked about ealier today?”
* * *
Solutions to Camp Chaos Puzzles
1. Here’s the shortest sequence of moves that does the trick:
2. Here’s one arrangement. There are others.
3. Bigshot is wrong. It is true that when swimming with the current, the
swimmer’s speed is increased by an amount that exactly compensates for the loss
of speed when swimming against the current, but their time is still affected,
because they spend longer swimming against the current than they do swimming
with it.
For example, suppose that the pool is 50 metres long, and that the swimmer
can swim at 5000 metres per hour in still water. Then it takes the swimmer (50 x
100)/5000 hours to swim 100 lengths: one hour, the time limit for a prize.
Suppose that the current flows, say, at 1000 metres per hour. Then the
swimmer’s speed is 6000 metres per hour when going with the current, and 4000
metres per hour when going against it. The total length of 5000 metres consists
of 2500 metres swum with the current and 2500 metres swum against it. So the
time taken is 2500/6000 + 2500/4000 hours, which is 25 mins + 37.5 mins, or 1
hour 2.5 mins, which is slower.
Bigshot’s error is especially obvious if the current flows faster than the
swimmer can swim. Then they would take infinitely long to complete the
marathon.
4. With the arrangement
1 2 3 4 5 6 7 8 9
18 17 16 15 14 13 12 11 10
opposite numbers in a pair add up to 19, which is one more than the number of
holes. The same is true for all similar arrangements. Since hole 7 is opposite
hole 16, their sum (23) is one more than the number of holes. So there are 22
holes, and Bert and Lynn Leisure Residence Rentals plc will be in deep trouble
with the Tuesday League.
5.
