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Programming Enigma Puzzles
It is the year 2100 and the Mars pioneers have built an agri-bubble in which they will be able to cultivate their own food. The crop is a form of grass that grows at a steady rate and can be harvested and turned into nutritious protein snacks (yum!). Now it is time to populate the planet.
Scientists have figured out that if there are 40 adults living in the bubble, the crop will only feed them for 20 days. However, with only 20 adults, the crop will keep them going for 60 days — so half as many adults can survive for three times as long! Why? Because without overharvesting, the crop is able to replenish itself.
Of course, the pioneers want a food supply that keeps the population sustained indefinitely. Based on the numbers above, how many people should be in the first Mars cohort?
A hero enters a cave. Inside is a monster with three numbered heads. It attacks! Our hero chops off a head, but two more heads grow in its place. One of the new heads attacks and the hero greets it with a quick chop, too. Standing back, he realises that every chop produces at least one prime-numbered head that, when multiplied by the number on the other new head, gives the number from the head that was chopped. He also notices that all the prime-numbered heads are friendly.
The story’s illustrator squints at the author’s scribbled notes. She can make out the numbers on two of the original three heads (418 and 651) but not the third. Reading ahead, she notices that when the hero collapses triumphant at the feet of the now fully friendly monster, all the heads show different numbers and their sum is 113.
“Aha!”, she declares, and draws the original monster with its three snarling, numbered heads.
What was the third number?
Scientists have been studying two rare monkey species in a forest.
In one part of the forest live the Equalis monkeys, which are split 50-50 between males and females. In another part of the forest are the Fraternis monkeys, of which exactly two-thirds are male — the evolutionary aspect of this isn’t yet known.
Both species are monogamous, with families coming in all shapes and sizes. Some parents stop at one offspring, but there are others with 10 or more, so some monkeys have lots of brothers, while others have none at all. The sex of any infant is independent of others in the family.
Among Equalis monkeys, which should expect to have more brothers, the males or the females? And how about the Fraternis monkeys?
When the giant town-hall clock chimed 2 o’clock, an ant resting by the number 2 woke from its nap. Spotting that the minute hand was edging towards it, the ant started walking clockwise round the rim of the clock face. Thinking it had escaped the minute hand, it was shocked when it caught up with the hand again. At that point, the ant turned round and walked anticlockwise back round the rim, at the same constant speed as before, reaching the minute hand for a second time after a further 15 minutes. At this point, it decided to give up and take another nap.
At what time did the ant stop walking?
The students at Yellow Brick High School for Girls couldn’t decide if their maths and drama teacher, Ms Gale, was a genius or just overworked when she announced the new school play, a “mathemusical” called The Wizard of Odds. But the real challenge, as usual, was in the casting, and the parents, students and faculty had various demands, summed up as follows:
1. If Megan doesn’t get the lead role, Dorothree, then Kasey will play either the Square Crow or the Ten Man.
2. If neither Leah nor Nicki are the Cowardly Line, Jane will will be Dorothree.
3. If Leah doesn’t get the Square Crow, Jane or Kasey will get Dorothree.
4. If Nicki isn’t the Ten Man and if Leah doesn’t get Dorothree, then Kasey will play the Wicked Witch of the Word Problems.
5. If Leah isn’t the Cowardly Line and if Nicki isn’t the Wicked Witch of the Word Problems, then Jane will be cast as the Square Crow.
Remembering that “if x, then y” doesn’t imply “if not x, then not y“, can you help Ms Gale accommodate this tornado of requests by assigning the roles?
I have a 12-hour digital number display alarm clock. As is normal on digital clocks, each of its four digits is constructed using seven possible segments.
I go to bed when the display is at its dimmest and awake when it is at its brightest.
How long am I in bed?
My son is obsessed with chess, and has been acting out the game’s moves everywhere we go, running like a bishop and jumping like a knight on tiled floors. He was tickled to see that on the number pad of my keyboard he could type 27 using a knight’s move, because the move from 2 to 7 is an L-shape, like a knight moves on a chessboard.
Alas, he can’t make 27 using a bishop move. Bishops move diagonally any number of spaces, so a bishop, using multiple moves, could make a number like 484 or 9157. In a similar fashion, a knight could make numbers such as 167 or 8349.
Yesterday, he made a happy discovery: a three-digit knight number that is exactly 27 more than a three-digit bishop number. (Actually, I found I could put another digit, call it “X”, at the front of my son’s numbers, and still have a knight number that is exactly 27 more than a bishop number).
What numbers did my son find?
Emma Neesha is a forgetful sort, and she has just locked herself out of her house with her keys still inside.
Not to worry, she installed keypads on both her house and car for such occasions. Unfortunately, she has also forgotten the four-digit code to her house.
This shouldn’t be a problem, because she keeps a code clue in her wallet. It says: “Four times the car’s four-digit code”.
Well, that is fine, but she has forgotten that one too. Fortunately, Emma is prepared: she has a clue written down for the car’s code as well. Pulling that one out, it reads: “The reverse of the house code”. Oh dear.
Can you help?
“Here’s your 21st birthday present”, said Amy.
“A bracelet?”, frowned Sam.
“Not just any bracelet, it is a magic number bracelet because I know you love numbers. See how it has got five beads, each with a different positive number on it. You can find all the numbers from 1 to 21. But to find most of them, you have to add together adjacent beads.”
“For example, to make the number 17 you add together these three beads”, she said, pointing to the beads in positions A, B and C on the diagram. “Other numbers are found by adding two, three or four adjacent beads. And, of course, to get 21, you add up all five”.
What are the five numbers on Sam’s bracelet?
“Have you written your thank-you letters, Kayleigh?”
“Not yet mum, just doing it now. Do I thank Amelia for the nail varnish, Beth for the book, Clara for the lip balm, Diaz for the pencils and Elinor for the sunglasses?”
“At least four of those are wrong.”
“Ah, then was it Amelia for the book, Beth for the lip balm, Clara for the pencils, Diaz for the nail varnish and Elinor for the sunglasses?”
“That’s better, but you’ve still made mistakes.”
“How about Amelia for the lip balm, Beth for the sunglasses, Clara for the pencils, Diaz for the book and Elinor for the nail varnish?”
“Even better, but still not full marks. Clara didn’t give you the pencils or the sunglasses!”
“I give up.”
Can you help?
Some town squares are designed as giant chessboards, but urban planner Dominica has paved her town’s new piazza with giant dominoes instead.
Picking different dominoes at random from a set, she laid them down flat to form a 7×7 square of numbers (pictured, below), leaving one space in the centre for a fountain.
Using the numbers on the diagram, can you draw the outlines of the dominoes that Dominica used, and figure out which dominoes she left out?
(Remember that a full set of dominoes contains every pair of numbers from 0-0 to 6-6. There were no duplicates).
University student Rick Sloth has spent his life avoiding work, and even though it is exam season he has no intention of mending his lazy ways.
He is studying palaeontology, which he thought might be an easy option when he signed up for it, as he loves dinosaurs, but he has now discovered that it requires rather more study than he was expecting.
It turns out there are 18 topics in the syllabus and his end-of-year exam will feature 11 essay questions, each on a different topic. Fortunately for Rick, candidates are only required to answer four questions in total.
Rick wants to keep his exam preparation to a bare minimum, while still giving himself a chance of getting full marks.
How many topics does he need to revise if he is to be certain that he will have at least four questions that he can tackle?
And can you come up with a general formula for the minimum number of topics you need to study based on the number of exam questions and topics in the syllabus?
At the shopping mall, while their mother’s attention is conveniently fixed on a window display, Jill furtively approaches her brother.
“Hey, what do you say to a race up to the next floor and back? Winner does the other one’s chores”.
“You’re on”, says Jack.
There are two escalators that move at the same speed, one going up and one going down, and also a regular set of stairs.
The children decide that each will choose on which of the three they want to race, but whatever they pick, they will have to run both up up and down on that choice. Jack knows he can run upwards and downwards at about the same speed (and much faster than the escalator).
Which of the three methods should he choose for the race: the up escalator, the down escalator or the stairs?
In the Zordik language, the seven days of the week start with Ardik (Monday). The other days are Bordik, Curdik, Deldik, Endik, Fordik and Gandik, but not exactly in that order.
In her Zordik class, teacher Miss Taik asked the students to recite the days in order, starting with Ardik. Sven called them out in alphabetical order.
“You got three in the right place”, said the teacher. “Kim, you have a go”.
“Deldik, Bordik, Ardik, Curdik, Endik, Gandik and Fordik”.
“Three right again. Help them, Raki”.
“Gandik, Deldik, Curdik, Bordik, Ardik, Fordik and Endik”.
“Unbelievable — you only got three right as well. Still, you now have all the information you need to work out the days of the week in order”.
What are they?
Penny Wise, chief financial officer of the Hartree Power Company, has decided to rent out surplus land beside its cooling towers, in an effort to boost her company’s annual income. The land, outlined in red on the plan above, was to have been for a fourth tower, which is now no longer required, plus the land between the three existing towers.
Her legal officer has been tasked with preparing the rental agreement, but is having difficulty in calculating the area of land for rent.
Can you help?
Amira presented her homework to her teacher:
“Wrong, Amira, please check your working.”
“I promise you it is right. It is just that I have used a code. Every digit used represents a different digit, and the same digit is always represented by the same ‘wrong’ digit. For example, maybe I replaced all the 6s with 4s. Or maybe I did something else…”
“You are giving me a headache, Amira.”
What is the correct sum?
In the TV number quiz show Down for the Count, four contestants are challenged to combine each of five number cards exactly once to achieve a target number. They are allowed to use standard arithmetical operations +, –, × and ÷ (as well as brackets, if required).
“I’ll take five cards from the top row”, requested one of the contestants, and the presenter Anne-Marie obligingly revealed these five numbers:
The studio computer then generated today’s challenge:
“Produce a whole number without any zeroes.”
No zeroes? Wow. Each of the four contestants thought hard, and after the timer ran out, each announced that they had used the five cards to produce a positive number smaller than 10. All four were different.
Which numbers did they get, and how?
While window-shopping at a toy store, my partner and I came across a set of dice that was partially obscured at the back of the shop’s display.
My partner took one look and bet me that I couldn’t tell them what the sum of all the touching faces between the dice would be. I accepted and gave the correct answer.
What was it?
“When exactly is a person supposed to celebrate their half birthday?”, wondered Lionel. “I mean, you could celebrate your 182/365th birthday, or your 183/365th birthday, but unless it is a leap year, the 1/2 fraction never arrives”.
“The world’s greatest mystery”, said Jill.
“But the good news is that if you write every date as a fraction, so 1 January is 1/365 and 2 January is 2/365 and so on, then my birthday falls on a day where that fraction is reducible”, says Lionel.
“You know, can be simplified, like 12/18 can be reduced to 2/3. My birthday fraction can be reduced, but the next day can be reduced even more, to numbers on the top and bottom that are even smaller”.
“I’ll be sure to celebrate by reducing the number of presents I get you”, says Jill.
When is Lionel’s birthday?
Click! The camera shutter opened and closed just as the creature’s head ducked back beneath the surface of the lake, creating a large ripple.
“I got it! I finally got a picture of the Loch Ness monster!”, exclaimed Lily. She looked at the result on her digital camera. “It’s blurry!”. She hung her head in defeat.
The boat passed directly over the spot where they saw the creature, but it was nowhere to be found. “How far away do you think it was when I took the picture?” Lily asked Amelia later that day.
“Well, we were travelling in a straight line at 2 metres per second towards where we saw Nessie, and it took us 5 seconds to reach that large ripple it created, and another 10 seconds to get to the other side of the ripple. So that means it was 5 seconds plus an additional 5 to the middle of the ripple, which would make it 20 metres!”.
“Sadly, I think your maths is as fuzzy as my photo,” said Lily.
How far away was the monster at the time the picture was taken?