Enigmatic Code

Programming Enigma Puzzles

Category Archives: puzzle#

Puzzle #61: Triple jump

From New Scientist #3283, 30th May 2020 [link] [link]

“My Auntie Connie just had triplets, three boys!”
“Wow, how old is she?”
“I dunno, but she’s really old.”
“Do you think the boys’ ages will ever catch up to your auntie’s? If you add all three together, I mean.”
“I’m not sure they’ll ever add up to her age exactly — I think it depends on how old she is now.”

Assuming they all live to a ripe old age, what are the chances that there will come a date in the future when the ages of the three boys add up exactly to their mother’s age?

(To be clear: your “age” is how old you were on your last birthday, so it is always a whole number).

[puzzle#61]

Puzzle #60: Mexican standoff

From New Scientist #3282, 23rd May 2020 [link] [link]

The Good, the Bad and the Bumbling have decided the only way to resolve their differences is with a three-way duel, aka a Mexican standoff. They stand in a triangle, each armed with a gun and unlimited ammunition. As you might expect, Good has the deadliest shot: he kills his target 99 per cent of the time. Bad is more hit-and-miss: his success rate is 66 per cent. And Bumbling, in his role as the comedy relief, only fatally hits the mark 33 per cent of the time. On a count of three, each will draw their gun and, using the best strategy they can, will keep shooting with the aim of being the last spaghetti westerner standing.

Roughly what is the chance that Bumbling will survive?

[puzzle#60]

Puzzle #59: Celebrate the differences

From New Scientist #3282, 16th May 2020 [link] [link]

Complete the diagram so that each of the nine circles contains a different digit from 1 to 9. Whenever two circles are connected by a straight line, the difference between the two numbers must be three or more (e.g. 5, 6, 8 and 9 can’t be connected to 7). The bottom-left square isn’t 1.

[puzzle#59]

Puzzle #58: Lego lockdown

From New Scientist #3281, 9th May 2020 [link] [link]

It is lockdown in my house and to keep the kids occupied, I have challenged them to find all the possible sequences when placing red 1×1 and blue 2×1 Lego blocks in a row.

There is only one way of making a row of length one (one red); there are two ways of getting a row of length two (B or RR); and three ways of getting a row of length three (BR, RB and RRR).

But after length three, the pattern seems to break down. There are five ways to get length four (BB, BRR, RBR, RRB and RRRR).

I’ve now set the kids the task of finding out how many ways there are of making a row of length 10. That should keep them busy. But their further challenge is to work out the pattern, so they can figure out the number of sequences for any length of row.

Can you help?

[puzzle#58]

Puzzle #57: Matchstick magic

From New Scientist #3280, 2nd May 2020 [link] [link]

Your challenge is to move two matchsticks to produce a calculation that gives an odd number.

How many solutions can you find?

[1-3: well done. 4-6: brilliant. 7-10: amazing. 11: exceptional]

[puzzle#57]

Puzzle #56: Diffy squares

From New Scientist #3279, 25th April 2020 [link] [link]

Diffy is a subtraction game. You choose four whole numbers between 1 and 12 and write them on the corners of a square. Then, you find the difference between numbers at neighbouring corners and write the answer at the midpoint (see above).

Join the midpoint numbers to form a diamond, then repeat the process until you end with four zeroes in a square (which always happens, eventually). In the example, there are five squares, but with the right starting numbers you can get more than five. Your challenge is to find whole numbers between 1 and 12 that will do this.

– You are a high achiever if you get more than six Diffy squares.
– You are a genius if you get 10 Diffy squares.

[puzzle#56]

Puzzle #55: Ton up

From New Scientist #3278, 18th April 2020 [link] [link]

How can you divide 100 into four parts such that: adding 4 to the first part, subtracting 4 from the second part, multiplying the third part by 4 and dividing the fourth part by 4 results in all parts having the same value as each other?

[puzzle#55]

Puzzle #54: Pyramid of possibilities

From New Scientist #3277, 11th April 2020 [link] [link]

 

In the ancient land of Aztekia, people are proud of their historic ziggurat. In it, each block bears a different number that is equal to the product of the two whole numbers on which it rests. Given the two numbers shown, can you complete the monument? Bear in mind that no two numbers are the same on these ziggurats.

[puzzle#54]

Puzzle #53: Painting by numbers

From New Scientist #3276, 4th April 2020 [link] [link]

When the famous artist Pablo Picossa held his final exhibition at the Galleria del Pardo, he wanted the public to experience his works in the order in which he had created them. Paintings from his early “Green” period were in room 1. From there, visitors should go to room 2 to see his Mauve works and then to the adjacent rooms 3, 4, 5 and so on, until they reached the Black paintings (generally viewed as Picossa’s darkest period) in room 9.

Alas, no details remain to indicate which room was where. Yet his widow Bella does recall a curiosity about the numbering of the rooms: the three-digit number formed by the top row added to the the number formed by the middle row equals the number formed by the bottom row.

Can you recreate Picossa’s gallery tour?

This is a rewording of the puzzle previously published in New Scientist as Tantalizer 467 (September 1976) and Enigma 328 (October 1985).

[puzzle#53]

Puzzle #52: Bus change

From New Scientist #3275, 28th March 2020 [link] [link]

I am about to get on the bus, but I don’t have the exact money for the £1 fare. The driver doesn’t give change so I hand over more than £1 and they keep the excess.

Once I have sat down, I realise that even though I didn’t hand over all my coins, the amount of money I had with me was the largest possible amount I could have had in change without being able to pay £1 (or any multiple of £1) exactly.

How much did I have?

[puzzle#52]

Puzzle #51: Birthday candles

From New Scientist #3274, 21st March 2020 [link] [link]

It is Tom’s 7th birthday and he has a cake with seven candles on it, arranged in a circle – but they are trick candles. If you blow on a lit candle, it will go out, but if you blow on an unlit candle, it will relight itself.

Since Tom is only 7, his aim isn’t brilliant. Any time he blows on a particular candle, the two either side also get blown on as well.

How can Tom blow out all the candles? What is the fewest number of puffs he can do it in?

[puzzle#51]

Puzzle #50: Crossing the river

From New Scientist #3273, 14th March 2020 [link] [link]

Petal is on her way to a country fair, to sell some vintage kitchenware belonging to her good friend Gretel. As she walks along the River Biddle admiring the view, Petal trips on a pair of oars left carelessly on the bank. A valuable wrought-iron kettle flies out of her hand and lands on one of the river’s many marshy islands.

From the river bank to the island is 3 metres directly across, and though the oars are sturdy enough to walk on, they are just short of reaching over the water.

How can Petal reach reach the island with the paddles and save Gretel’s metal kettle from its muddy peril?

[puzzle#50]

Puzzle #49: The tree in the snow globe

From New Scientist #3272, 7th March 2020 [link] [link]

I have a snow globe that is a hollow hemisphere. At its highest point, it is 10 centimetres tall, and in the centre stands a tree that is 6 cm tall. How far away from the centre can the tree be moved and still stand upright?

[puzzle#49]

Puzzle #48: Seeing red

From New Scientist #3271, 29th February 2020 [link] [link]

The traffic lights near me are annoying: they are green for just 10 seconds and red for 90 seconds. I go through them only on green on my bike every day and I first see the lights as I approach around a bend when I am 15 seconds away. I get upset if I miss a green light that I could have got through. I can speed up by about 25 per cent or I can slow down.

What should my strategy be if the lights are green when I first see them? And what if they are red? And how often might I get upset?

[puzzle#48]

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#47]

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#46]

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#45]

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#44]

Puzzle #43: Dividing Grandma’s field

From New Scientist #3266, 25th January 2020 [link] [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#43]

Puzzle #42: The card conundrum

From New Scientist #3265, 18th January 2020 [link] [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#42]

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