Tag Archives: logic

Rock, Paper, Scissors Problem

Here is another problem from the Sherlock Holmes puzzle book by Dr. Watson (aka Tim Dedopulos).

“Wiggins grinned at me. ‘You’ve not played Rock Paper Scissors before, Doctor?’

‘Doesn’t ring a bell,’ I told him.

‘Two of you randomly pick one of the three, and shout your choice simultaneously. There are hand gestures, too. If you both get the same, it’s a draw. Otherwise, scissors beats paper, paper beats rock, and rock beats scissors.’

‘So it’s a way of settling an argument,’ I suggested.

‘You were brought up wrong, Doctor,’ Wiggins said gravely. ‘Look, try it this way. I played a series of ten games with Alice earlier. I picked scissors six times, rock three times, and paper once. She picked scissors four times, rock twice, and paper four times. None of our games were drawn.’ He glanced at Holmes, who nodded. ‘So then, Doctor. What was the overall score for the series?’ ”

Answer.

See the Rock Paper Scissors Problem for solutions.

(Update 7/29/2021)  This problem in a different guise was presented by Futility Closet (7/28/2021) and attributed to Yoshinao Katagiri in Nobuyuki Yoshigahara’s Puzzles 101: A Puzzlemaster’s Challenge, 2004.

Do I Avoid Kangaroos?

This is a fun logic puzzle from one of Ian Stewart’s many math collections.  I discovered that the problem actually is basically one of Lewis Carroll’s examples from an 1896 book:

  1. The only animals in this house are cats.
  2. Every animal that loves to gaze at the moon is suitable for a pet.
  3. When I detest an animal, I avoid it.
  4. No animals are meat-eaters, unless they prowl by night.
  5. No cat fails to kill mice.
  6. No Animals ever take to me, except those in this house.
  7. Kangaroos are not suitable for pets.
  8. Only meat-eaters kill mice.
  9. I detest animals that do not take to me.
  10. Animals that prowl at night love to gaze at the moon.

If all these statements are correct, do I avoid kangaroos, or not?

Answer.

See Do I Avoid Kangaroos? for solutions.

Swallowing Elephants

This is a simple logic puzzle from one of Ian Stewart’s many math collections.

  1. Elephants always wear pink trousers.
  2. Every creature that eats honey can play the bagpipes.
  3. Anything that is easy to swallow eats honey.
  4. No creature that wears pink trousers can play the bagpipes.

Therefore:

Elephants are easy to swallow.

Is the deduction correct, or not?

Answer.

See Swallowing Elephants for a solution.

The Squirrel Puzzle

For a change of pace, here is an early puzzle from Alex Bellos in The Guardian.

“Happy New Year guzzlers!  Today’s first problem concerns squirrels. Have a nibble—it’s not too hard a nut to crack.

The Squirrel King has buried the Golden Acorn beneath one of the squares in this 6x6 grid. Three squirrels—Black, Grey and Red—are each standing on a square in the grid, as illustrated.

(Note: for the purposes of today, squirrels can speak, hear, read, count and are perfect logicians. They can also move in any direction horizontally and vertically, not just the direction these cartoons are facing. They all can see where each other is standing, and the cells in the grid are to be considered squares.)

The Squirrel King hands each squirrel a card, on which a number is written. The squirrels can read only the number on their own card. The King tells them: ‘Each card has a different number on it, and your card tells you the number of steps you are from the square with the Golden Acorn. Moving one square horizontally or vertically along the grid counts as a single step.’ (So if the acorn was under Black, Black’s card would say 0, Grey’s would say 4, and Red’s 5. Also, the number of steps given means the shortest possible number of steps from each squirrel to the acorn.)

The King asks them: ‘Do you know the square where the Golden Acorn is buried?’ They all reply ‘no!’ at once.

Red then says: ‘Now I know!’

Where is the Golden Acorn buried? …”

See the Squirrel Puzzle

Math and Literature

For a number of years I have collected excerpts that portray mathematical ideas in a literary or philosophical setting. I had occasion to read a few of these on the last day of some math classes I was teaching, since there was no point in introducing a new subject before the final exam.

I thought it might be interesting to present some of these excerpts now. They roughly fall into three categories: logic, infinities (Zeno’s Paradoxes, infinite regress), and permutations.

See Math and Literature

(Update 11/16/2019) Continue reading →

Meditation on “Is” in Mathematics II – Mathematical Reality

This post continues a meditation on the nature of mathematics begun in Part I. It involves the perennial question about whether mathematics is invented or discovered, and consequently evokes questions about mathematical reality. This subject is probably of little interest to most people, and even most mathematicians. But the extremely heavy involvement of mathematics in the descriptions of quantum mechanics, and the even more mathematically abstruse excursions into ideas such as string theory in an effort to wed quantum mechanics to general relativity, force us to confront the central place mathematics has in “explaining” our physical reality. Of course, this essay has no definitive answers, and leaves the situation as a mystery.  See Meditation on “Is” in Mathematics II – Mathematical Reality.

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