THE faded, peeling sign at the main gateway read: 鈥淲elcome to Bert and Lynn鈥檚
Holiday Camp. Take a break with family and pets in a friendly relaxed
补迟尘辞蝉辫丑别谤别.鈥�
Inside the gate, of course, the atmosphere was anything but relaxed. The camp
was firmly in headless chicken mode鈥攁nd the customers hadn鈥檛 even started
to arrive.
The trouble was that the camp鈥檚 manager, Duff Bigshot, couldn鈥檛 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 Jobsworthy.
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It didn鈥檛 help that Bigshot had the nagging feeling that he had forgotten
something extremely important.
Jobsworthy was setting out the buckets of dye for the Punk Poodle Parade. It
was a long-standing tradition at Bert and Lynn鈥檚 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鈥檚 drunken revelry. No doubt he should have obtained his guests鈥� 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鈥檚 guests, awarding a prize of
拢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. Jobsworthy 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. 鈥淛obsworthy, how many times do I
have to tell you that I don鈥檛 want the colours bunched up like that? It ruins
the stage decor.鈥�
鈥淪orry, Mr Bigshot. How would you like them arranged?鈥�
鈥淚 want red and blue buckets to alternate. The one thing you have got right
is the two empty seats鈥攐ne for the contestant and one for their precious
punk poodle. Next to each other at one end, naturally.鈥�
鈥淥h, right,鈥� said Jobsworthy, picking up a bucket at random and placing it on
the floor. He reached for another.
鈥淲hat are you doing now?鈥� Bigshot snapped.
鈥淢oving the buckets, sir.鈥�
鈥淐an nobody here use any initiative?鈥� said Bigshot.
鈥淣o, sir,鈥� replied Jobsworthy.
鈥淭hat was a rhetorical question, Jobsworthy.鈥�
鈥淲ith respect, it was a rhetorical answer sir.鈥�
Bigshot decided to be more explicit. 鈥淵ou don鈥檛 need to put any of the
buckets on the floor, Jobsworthy. 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鈥檝e rearranged the buckets
the way I told you.鈥�
He flounced out, leaving Jobsworthy staring at the buckets and scratching his
head in bewilderment.
Vowing to demote Jobsworthy 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鈥檚 four luxury kennels (see
figure).
鈥淣o, no, no!鈥� shouted Bigshot in irritation.
鈥淣o what?鈥� asked Mann.
鈥淣ot like that!鈥�
鈥淏ut you told me to wall off the kennels, Mr B,鈥� protested Mann.
鈥淚 meant you should wall them off from each other,鈥� said Bigshot. 鈥淣ot from
the outside world.鈥�
鈥淥h. Shall I demolish this wall I鈥檝e just built, then, Mr B?鈥�
鈥淣o, no. No. Definitely not. No point in wasting bricks. No, you鈥檒l just have
to build some more walls. And I don鈥檛 want complaints from guests like we had
three years ago when Mrs Boomthumper鈥檚 towels were 6 millimetres shorter than Mr
Rubbingham-Snyde鈥檚. 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?鈥�
鈥淩ight, Mr B, yup, got that. Um, how many new walls do you want?鈥�
Bigshot looked at the kennels. 鈥淭hree 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鈥檙e part of the same wall. OK?鈥�
鈥淕ot that, Mr B.鈥�
鈥淕ood. And stop calling me Mr B, OK?鈥�
Mann grinned. 鈥淛ust as you say, Mr B.鈥�
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鈥攓uite a steep slope, as it happened.
The senior pool manager, Lily Padd, denied all blame. 鈥淚鈥檓 sorry, Mr
Bigshot,鈥� she simpered, 鈥渂ut my job is to maintain the pool, not supervise its
肠辞苍蝉迟谤耻肠迟颈辞苍.鈥�
鈥淏ut it鈥檚 been built on a hillside!鈥�
鈥淵ou鈥檒l have to discuss that problem with Mr Mann, Mr Bigshot. Planning is
not my department, I鈥檓 afraid.鈥� She sniffed haughtily.
鈥淐an鈥檛 do that, Lily. I鈥檝e left him building walls round the luxury kennels.
Damn, and we鈥檝e got the freestyle swimming marathon on the opening day of the
season, too.鈥�
鈥淐an鈥檛 they swim in the pool as it is, sir?鈥�
鈥淣o, Lily, they can鈥檛, because one end is only 10 centimetres deep.鈥�
鈥淲ell, if you鈥檙e going to be picky鈥︹��
Bigshot snapped his fingers. 鈥淗ow fast can we recirculate the water?鈥�
Lily shrugged. 鈥淭he pumps are very powerful. As fast as you want,
谤别补濒濒测.鈥�
鈥淥K, 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.鈥�
Lily pursed her lips. 鈥淢mmmm. Remember, we only give out the prize if the
winner swims a hundred lengths in under an hour鈥攁nd usually they just
manage it. Won鈥檛 the current slow the swimmers down? That would be unfair.鈥�
鈥淣ot at all,鈥� said Bigshot in triumph. 鈥淚t 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鈥檛 change.鈥�
Lily looked unhappy. I鈥檓 not sure that鈥檚 right, sir.鈥�
Bigshot glared at her. 鈥淣onsense!鈥� He paused. 鈥淥K, cleverclogs: if I鈥檓 so
wrong, you tell me why!鈥�
What next, Bigshot thought irritably, when Dot Ball, sport and
sandwich-filling administrator, rushed up and grabbed him by the arm.
鈥淢r Bigshot, Mr Bigshot, come quickly!鈥�
Bigshot glared at her. 鈥淣ot now, Dot.鈥�
鈥淏ut it鈥檚 crucially important!鈥�
Bigshot stopped, and sighed. 鈥淥K, Dot. Mmm . . . you wouldn鈥檛 have any idea
whether I鈥檝e forgotten something, would you?鈥�
鈥淭he wet wetsuit contest?鈥�
鈥淣o, that鈥檚 all ready to roll. Something less obvious, maybe? No, no, of
course not, forget I ever mentioned . . . Now, what鈥檚 all the fuss about?鈥�
She looked close to tears. 鈥淭he crazy golf.鈥�
鈥淭he what?鈥�
鈥淚 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鈥攐dd ones on one side, even ones
on the other, all in ascending order.鈥�
Bigshot nodded. 鈥淩ight. So what鈥檚 he done?鈥�
鈥淗e鈥檚 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鈥︹�� 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. 鈥淪o? Does it matter?鈥�
Dot鈥檚 fingers gripped his arm more tightly. 鈥淵es, it does. Not the order, but
the number of holes. Maxdoch鈥檚 arranged them in opposite pairs along the two
sides of the plot, all right, but I鈥檓 convinced that he has put in more than 18
丑辞濒别蝉!鈥�
鈥淎h.鈥� Bigshot had come across the identical problem a few years before.
鈥淵ou鈥檙e worried that our guests will be disqualified from the North Dorkshire
Crazy Golf Tuesday League play-offs.鈥�
鈥淓xactly,鈥� said Dot. Dear Duff, it was good to see that he was so
understanding.
鈥淢mmph. As I recall, they鈥檒l be OK as long as we have between 17 and 21
holes, inclusive. Yes?鈥�
鈥渊别蝉.鈥�
鈥淭hen how many have we got?鈥�
Dot鈥檚 eyes swam. 鈥淭hat鈥檚 the trouble,鈥� she wailed. 鈥淚 can鈥檛 remember.鈥�
鈥淲ell, run off and find out.鈥�
鈥淭ricky. I promised Cook that I鈥檇 help out with the Esperanto dinner menus.鈥�
She was a picture of indecision. 鈥淟ook, I do remember that Maxdoch had put the
seventh hole immediately opposite the sixteenth. Maybe that will help?鈥�
鈥淥h my God!鈥� cried Bigshot in despair. 鈥淚 don鈥檛 believe it!鈥�
He had arrived at the ballroom to find the dance floor laid out as shown
below.
鈥淲hat鈥檚, like, your personal difficulty with this?鈥� asked the Indoor Leisure
Activities Coordination Officer, Lars Tango. 鈥淒on鈥檛 you, like, relate to the
postmodern Kasparovian Deepest Blue motif?鈥�
鈥淭he chess motif is fine,鈥� said Bigshot, who had asked for it months ago.
鈥淭he shape isn鈥檛.鈥�
鈥淏ut, I mean, you said you, like, wanted it sort of, well, square. Ish.鈥�
Bigshot stared at him.
鈥淥h.鈥� Realisation dawned. 鈥淵ou meant, like, really square? Really, really
square? I mean, my God, plain square?鈥�
Bigshot, assuming a vulture-like posture, continued to stare. Tango
turned bright pink. 鈥淥h, 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?鈥�
Bigshot nodded. 鈥淵ou got it. Not two squares. One.鈥�
鈥淥h. 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鈥檛 you?鈥�
Bigshot sighed once more. 鈥淟ars, it鈥檚 not asking very much if I want you to
sort me out a single 10 by 10 square of chequered flooring, is it?鈥�
Tango slumped in defeat. 鈥淗onestly, it鈥檚, 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鈥檇 make your mind up!鈥�
Bigshot decided that it wasn鈥檛 worth arguing. 鈥淟ook, Lars, there鈥檚 got to be
some way to cut up those two squares and reassemble the pieces to make a 10 by
10 chessboard.鈥�
Tango thought for a moment. 鈥淥h, 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鈥︹��
鈥淒on鈥檛 be silly,鈥� said Bigshot. 鈥淚鈥檓 sure you can manage with a lot fewer
pieces than that.鈥�
Bigshot breathed a sigh of relief. By the skin of his teeth, he鈥檇 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鈥o, silly, forget it.
He felt a tap on his shoulder and turned. It was Pansy Petal. 鈥淚 hope you鈥檙e
not going to tell me that the Esperanto menus aren鈥檛 printed yet,鈥� he joked.
Petal didn鈥檛 laugh.
鈥淥h my God鈥攖hey鈥檙e not?鈥�
鈥淭he Esperanto menus are fine,鈥� said Pansy.
鈥淥h, good. Er, we鈥檝e run short of beds?鈥� Bigshot chuckled. Now that would be
a real disaster. But of course the beds were counted every 10 years.
鈥淏eds are fine.鈥� He breathed a small sigh of relief. 鈥淏ut there isn鈥檛 a
single mattress in the whole camp.鈥�
Bigshot snapped his fingers in delight. 鈥淥f course! That鈥檚 what I鈥檇
forgotten!鈥� Then his delight at remembering gave way to panic as he realised
what he鈥檇 done. There was a long, awkward silence as he desperately tried to
salvage the situation. Aha! 鈥淓r, Pansy?鈥�
鈥淵es, Mr Bigshot?鈥�
鈥淒o we still have those lovable jumbo inflatable teddy bears that you and I
joked about ealier today?鈥�
* * *
Solutions to Camp Chaos Puzzles
1. Here鈥檚 the shortest sequence of moves that does the trick:
2. Here鈥檚 one arrangement. There are others.
3. Bigshot is wrong. It is true that when swimming with the current, the
swimmer鈥檚 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鈥檚 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鈥檚 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.
