Here is a nice logic puzzle from 2014 Futility Closet.
“Only one of these statements is true. Which is it?
_________A. All of the below
_________B. None of the below
_________C. One of the above
_________D. All of the above
_________E. None of the above
_________F. None of the above”
See Pointing Fingers for solutions.
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
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.
(Update 11/16/2019) Continue reading
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.
