# Enigmatic Code

Programming Enigma Puzzles

## 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 #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 #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?

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#### 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?

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#### 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?

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#### Puzzle #38: Meaningful matches (1)

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

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#### Puzzle #39: Meaningful matches (2)

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

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

## Puzzle #15: Lines through the chessboard

From New Scientist #3241, 3rd August 2019 [link] [link]

Linus is using a thin felt-tip pen and a ruler to draw straight lines on a conventional 8×8 chessboard. With eight lines, he can easily ensure that a line passes through every square on the board. For instance, he can just draw a line through the middle of each row of squares, which means each line would go through eight squares. But a line can pass through more than eight squares – for example, the one in the illustration goes through nine – so Linus wants to find a way to cut through all 64 squares with fewer than eight lines.

Can you help?

[puzzle#15]

## Puzzle #11, #12: Lunar years, Hole of the moon

From New Scientist #3238, 13th July 2019 [link] [link]

#### Lunar years

My twin sister went to live on the moon on our 30th birthday. From then on, she counted a year as 365 sunrises, just as we do on Earth. I am now 60. Which birthday did she last celebrate?

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#### Hole of the moon

I punched a hole 6 millimetres across in a piece of paper and held it at arm’s length to look at the full moon. I was pleased to find that the moon filled the hole perfectly. If the moon is 3500 kilometres across, can you estimate how far away it is?

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[puzzle#11] [puzzle#12]

## Puzzle #03: Cube shadow

From New Scientist #3230, 18th May 2019 [link]

At midday at her home in Ecuador, Natalia holds a solid cube 1 metre above the ground and it casts a shadow. She rotates the cube a bit and finds that the smallest shadow she can create is a square. What is the shape of the largest shadow she can produce with the cube at noon and how much bigger is it than the square shadow?

[puzzle#03]

## Puzzle #01: The book of numbers

From New Scientist #3228, 4th May 2019 [link] [link]

Meera plans to write a book (in English) containing all the whole numbers from zero to infinity in alphabetical order. She knows this will take her a very long time, but she makes a start. She figures that first on her alphabetical list is the number eight. After a while, she tires of the task and jumps to the last page and starts working backwards. She reckons that the last entry will be zero.

Curiously, even though this book will take forever to finish writing, it is possible to state which number will be listed second, and which will be second-last.

What are those two numbers?

(By the way, when Meera wants to write numbers bigger than the quadrillions (numbers with 15 digits), she string numbers together, for example “one billion trillion” or “five million million quadrillion”).

There appears to be a new sequence of puzzles appearing in New Scientist. (Similar to the Tantalizer and Puzzle sequence that appeared from 1967? up to 1978, in that it is not a prize puzzle. The solution will be published next week).

[puzzle#01]