Enigmatic Code

Programming Enigma Puzzles

Category Archives: puzzle#

Puzzle #47: Geometra’s tomb

From New Scientist #3270, 22nd February 2020 [link] [link]

Long before the invention of satnav, the great explorer Asosa Lees embarked on a trek across the square desert of Angula in a quest to find the lost tomb of Geometra, which lay somewhere along the line marked A.

Lees had nothing but the crude and incomplete diagram shown and some basic instructions: proceed south-west for 100 kilometres, and then turn left. The only other information she had was that at the moment she turned left, the distance to the south-west corner of the desert was 100 kilometres further than the distance to the south-east corner.

To reach the tomb, Lees needed to head in precisely the right direction. Fortunately using her knowledge of geometry she was able to take the correct bearing.

At what angle did she head off towards the tomb?


Puzzle #46: Pi-thagoras

From New Scientist #3269, 15th February 2020 [link] [link]

Pythagoras’s theorem says that for any right-angled triangle, the square of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the other two sides.

There are some right-angled triangles whose sides are all whole number lengths. The simplest and best known is the “3-4-5” triangle (3² + 4² = 5²).

I have drawn a circle that fits precisely inside a 3-4-5 triangle. What is the area of the circle? Have a guess. And then see if you can prove that you are right.


Puzzle #45: Beetles on a clothes line

From New Scientist #3268, 8th February 2020 [link] [link]

Peg beetles are a rare species with rather odd behaviour. As any peg beetle expert will know, these beetles always walk at 1 metre per minute, and when two beetles meet, they immediately reverse direction.

Six peg beetles are on a 2-metre-long clothes line, some walking left to right and others right to left (as the diagram shows). As we join the action, beetle A is at the left-hand end of the line and walking towards the right, while beetle F is at the right-hand end, walking left.

When a beetle reaches the end of the clothes line, it drops off onto the ground.

Which two beetles will be the last to drop off the clothes line, and how long will it be before that happens?


Puzzle #44: Elevator pitch

From New Scientist #3267, 1st February 2020 [link] [link]

On the way back from a party the other day, my daughter and I got into an elevator. I was holding a cup of water with an ice cube floating in it, while my daughter was admiring her helium-filled balloon as it floated above her on a slack string. Our only company in the elevator was a spider, dangling from the lift’s ceiling on a thin thread of silk. As the lift accelerated upwards, what did we see happening to the balloon, the ice cube and the spider?


Puzzle #43: Dividing Grandma’s field

From New Scientist #3266, 25th January 2020 [link]


Two brothers have inherited a plot of land from their grandmother. The map shows that the land is made up of five identical squares, and the green dots indicate the location of four old oak trees.

There are two stipulations in Grandma’s will:

First, the land must be divided so that the brothers get exactly half of the area each, and;
Second, each brother should have two of the trees on their land.

The brothers would love to divide the land with a single straight fence from one edge to another. Can you find a line for the fence that fulfils everyone’s wishes — and without you needing to do any measurement?


Puzzle #42: The card conundrum

From New Scientist #3265, 18th January 2020 [link]

Carl scribbled down an equation that contained only numbers and the letter X on a scrap of paper and left it on a table:

Bob found the card and realised that this was just a straightforward algebra problem. “I’ve found the solution”, he announced a minute later, dropping the card back on the table and leaving the room. Amy overheard him, walked over and picked up the card. After a while she announced: “That’s strange, I’ve found two solutions”.

Even stranger, Amy’s solutions were both different to Bob’s.

What were the solutions that Bob and Amy found?


Puzzle #41: Hen party dorm

From New Scientist #3264, 11th January 2020 [link]

Ten friends have rented a dormitory for the night of a hen party. Each person picks a bed for the night before heading out on the town. At 2 am they start heading home a little the worse for wear.

Amy, the first to arrive back at the dorm, can’t remember which bed she chose, so she picks one at random. The next person to return, Bethan, heads for her own bed, but if she finds it has already been taken, she randomly picks another.

The remaining friends adopt the same approach of going to their bed if it is available and randomly picking another if it isn’t. Janice is the last to get home. What is the chance that her own bed is still empty? And was Janice more or less likely to find the bed she first chose empty than Iona, who got back just before her?


Puzzle #40: Light bulb moment

From New Scientist #3263, 4th January 2020 [link] [link]

A tall office building is being rewired. There is a staircase, but the lift is out of action.

There are four identical-looking wires, A, B, C and D, feeding into a pipe in the ceiling of the basement. You are reasonably confident that it is those same four wires that emerge from a pipe on the top floor. Unfortunately the wires have become tangled, so it isn’t known which wire becomes 1, 2, 3 or 4.

To find out, you can join two wires together in the basement (for example A and C) and you can attach two wires at the other end to a light bulb and battery (for example 1 and 3). If the bulb lights, you have made a circuit.

Starting in the basement, what is the smallest number of light bulb flashes that you need in order to figure out which wire is which? And how many times do you need to climb the stairs?


Puzzle #35, #36, #37, #38, #39: A bunch of brain teasers

From New Scientist #3261, 21st December 2019 [link] [link]

Puzzle #35: Christmas gifts

Q1: By the twelfth day of Christmas, my true love has given me 12 partridges in a pear tree. But which gifts have I received the most of?

Q2: I want to give all the gifts back. Starting on 26 December 2019, I am going to give one of them to my true love every day. On which date will I give them my final gift?


Puzzle #36: All squares (1)

I met Natalie the other day. She wasn’t prepared to tell me her age, but she did tell me that in the year N², she will turn N years old.

In what year was she born?


Puzzle #37: All squares (2)

Can you work out (68² – 32²)/(59² – 41²) without using a calculator?

And can you do it without having to square any of the numbers?


Puzzle #38: Meaningful matches (1)

The figure below has four equilateral triangles. Move two matchsticks to get only three equilateral triangles.


Puzzle #39: Meaningful matches (2)

The figure below is composed of 29 matchsticks. Move two matchsticks to get a correct multiplication result.


[puzzle#35] [puzzle#36] [puzzle#37] [puzzle#38] [puzzle#39]

Puzzle #34: Ant on a tetrahedron

From New Scientist #3259, 14th December 2019 [link] [link]

Three short-sighted spiders are clustered at the vertex of a wire frame in the shape of a tetrahedron. The spiders know that there is an ant walking around the frame, but they have no idea where it is. They will only be able to spot it when they are practically on top of it. The ant, on the other hand, has excellent eyesight and can plan its route accordingly to avoid the spiders. Given that the ant walks slightly slower than the spiders, is there a way for the ant to escape the spiders indefinitely? Or can the spiders find a strategy to be certain of catching the ant?


Puzzle #33: The mountain pass

From New Scientist #3259, 7th December 2019 [link] [link]

Aaron has spent the night camped at the foot of a mountain, while Bonnie camped at the summit. In the morning, Bonnie sets off down the path to base camp at exactly the same time as Aaron begins his ascent.

At midday they pass each other and nod a greeting, both of them maintaining their constant walking pace. Bonnie gets to the bottom at 4pm and sets up camp, but it isn’t until 9pm that Aaron finally reaches the top.

What time did the two hikers set off in the morning?


Puzzle #32: Rearranging books

From New Scientist #3258, 30th November 2019 [link] [link]

Once a week, it is Jordie’s job at the library to put books back in order on the shelves.

This week, he finds that the 10-volume encyclopedia has been mixed up in the order shown above. He has to put them back in order, and since the books are heavy, he wants to move as few volumes as possible.

A move consists of taking a book off the shelf and sliding the other books to the side to make space, if necessary. What is the smallest number of moves he needs to make to rearrange the books in the order 1 to 10 from left to right?


Puzzle #31: Three hats

From New Scientist #3257, 23rd November 2019 [link] [link]

Ariana, Beverley and Cassie are standing in a line. They know that two of them are wearing black hats and one is wearing a white hat — or vice versa — in an arrangement like the one shown above.

Beverley and Cassie can see the hats in front of them but not behind, while Ariana can’t see any hats. They can only say “white” or “black” to announce their own hat colour.

Who will be able to confidently state their hat’s colour first? And who will be second?


Puzzle #30: Sticking in a pin

From New Scientist #3256, 16th November 2019 [link] [link]

Sachin tells me that the four-digit PIN that he uses for his credit card has an unusual property. When he enters his PIN into a calculator and squares it, the last four digits of the answer are also his PIN. He tells me that exactly one of the digits in his PIN is a zero, but he won’t tell me which position it is in.

What is Sachin’s PIN?


Puzzle #29: How many strips?

From New Scientist #3255, 9th November 2019 [link] [link]

How many 3×1 strips, like the example pictured [right], can be cut out of this piece of wood [left]?


Puzzle #28: A well-timed nap

From New Scientist #3254, 2nd November 2019 [link] [link]

I keep an analogue clock by my bed. One afternoon, I had a nap. When I drifted off to sleep, the minute hand was pointing directly at one of the 12 numbers on the clock face, and the number of minutes past the hour was exactly the same as the angle (in degrees) between the hour and minute hands.

Later that day, when I woke up, I noticed the same was true again.

How long had I been asleep?


Puzzle #27: The goblin game

From New Scientist #3253, 26th October 2019 [link] [link]

Annie and Beth are about to play “Goblin”. Like snakes and ladders, it is a game played on a 10 × 10 grid of squares numbered from one to 100. Players start with their counter off the board (next to square one) and take it in turns to roll a single die, aiming to be the first to get to square 100.

However, instead of snakes or ladders, there is just one hazard: a goblin. Each player gets one goblin and is allowed to place it on any square they want (apart from square 100) before the game starts.

If you land on your opponent’s goblin, you lose, and the same goes for your opponent. If a player lands on their own goblin, they are safe. If neither player lands on a goblin, the first to get to 100 wins (an exact final roll isn’t required, just getting to the 100 square is enough).

Annie, who has never played before, decides to place her goblin on square 31, because that is her lucky number.

Where should Beth place her goblin to have the maximum chance of winning?


Puzzle #26: Evening out

From New Scientist #3252, 19th October 2019 [link] [link]

The figure above is composed of 15 matchsticks. Move 2 matchsticks to get a 3-digit number with all the digits even numbers. Find them all!


Puzzle #25: Car crash maths

From New Scientist #3251, 12th October 2019 [link] [link]

Two cars of the same model, one blue, one yellow, are on a motorway in the UK. The blue car is in the inside lane travelling at 70 miles per hour*, which is the speed limit. The yellow one is speeding in the outside lane at 100 mph.

At the instant when they are neck and neck, both drivers see a fallen tree across the road some distance ahead. Both immediately brake, each applying the same constant braking force. The blue car manages to stop centimetres short of the tree. To the nearest 10mph, at what speed does the yellow car hit the tree?

a) 10 mph
b) 30 mph
c) 50 mph
d) 70 mph

Use your intuition (particularly if you are a driver) to have a guess. Then work out the answer to see if you were right.

* Alternatively, call the starting speeds 70 kilometres per hour and 100 km/h, the number in the solution will be the same.


Puzzle #24: Three stamps

From New Scientist #3250, 5th October 2019 [link] [link]

I’m on holiday in the lovely country of Philitaly, and planning to send plenty of postcards because postage is very cheap. But the country only allows up to three stamps on any letter.

Can you tell me which three denominations of stamps would allow me to cover any cost of postage from 1 cent to 15 cents inclusive?

And which four stamp denominations would allow all values from 1 to 24 cents?


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