## Tag Archives: Ian Stewart

### What Day is it?

Yesterday, Dad got confused about which day of the week it was. “Whenever we go on holiday, I forget,” he said.

“Friday,” said Darren.

“Saturday,” his twin sister Delia contradicted.

“What day is it tomorrow, then?” asked Mum, trying to sort out the dispute without too much stress.

“Monday,” said Delia.

“Tuesday,” said Darren.

“Oh, for heaven’s sake! What day was it yesterday, then?”

“Wednesday,” said Darren.

“Thursday,” said Delia.

“Grrrrrr!” said Mum, doing her famous Marge Simpson impression. “Each of you has given one correct answer and two wrong ones.”

What day is it today?

More fun later,

Nalin Pithwa

(Ref: Prof. Ian Stewart’s Cabinet of Mathematical Curiosities)

### Archimedes, you old fraud!

“Give me a place to stand, and I will move the Earth.” So, famously, said Archimedes, dramatizing his newly discovered law of the lever. Which in this case takes the form

Force exerted by Archimedes distance from Archimedes to fulcrum equals

Mass of Earth distance from Earth to fulcrum.

Now, I don’t think Archimedes was interested in the position of the Earth in space, but he did want the fulcrum to be fixed. (I know he said ‘a place to stand’, but if the fulcrum moves, all bets are off, so presumably that’s what he meant.) He also needed a perfectly rigid lever of zero mass, and he probably did not realize that he also needed uniform gravity, contrary to astronomical fact, to convert mass to weight. No matter, I don’t want to get into discussions about inertia or other quibbles. Let’s grant him all those things. My question is: when the Earth moves, how  far does it move? And, can Archimedes achieve the same result more easily?

(Ref: Prof Ian Stewart’s Cabinet of Mathematical Curiosities).

More later,

Nalin Pithwa

### The Missing Symbol

Place a standard mathematical symbol between 4 and 5 to get a number greater than 4 and less than 5.

(Another precious gem from Prof Ian Stewart).

(culled by)

Nalin Pithwa

### MacMahon’s Squares

This puzzle was invented by the combinatorialist P.A. MacMahon in 1921. He was thinking about a square that has been divided into four triangular regions by diagonals. He wondered how many different ways there are to colour the various regions, using three colours. He discovered that if rotations and reflections are regarded as the same colouring, there are exactly 24 possibilities. Find them all.

Now, a 6 x 4 rectangle contains 24 1 x 1 squares. Can you fit the 24 squares together to make such a rectangle, so that adjacent regions have the same colour, and the entire perimeter of the rectangle has the same colour?

(Thanks to Prof. Ian Stewart for putting this in his cabinet and I pulled it out of it !! :-))

Nalin Pithwa

### Fair Shares

In 1944, as the Russian army fought to reclaim Poland from the Germans, the mathematician Hugo Steinhaus, trapped in the city of Lvov, sought distraction in a puzzle. As you do.

The puzzle was this. Several people want to share a cake (by all means, replace that by a pizza if you wish). And, they want the procedure to be fair, in the sense that no one will feel that they have got less than their fair share.

Steinhaus knew that for two people there is a simple method: one person cuts the cake in two pieces, and the other chooses which one they want. The second person can’t complain, because they made the choice. The first person also can’t complain — if they do, it was their fault for cutting the cake wrongly.

How can three people divide a cake fairly?

Ref: Professor Ian Stewart’s Cabinet of Mathematical Curiosities

More fun coming,

Nalin Pithwa

### A Question of Breeding

Ref: Professor Ian Stewart’s Cabinet of Mathematical Curiosities

Farmer Hogswill went to the village tete, where he met five of his friends: Percy Catr, Dougal Dogge, Benjamin Hamster, Porky Pigge and Zoe Zebra. By a remarkable coincidence — which was a constant source of amusement — each of them was an expert breeder of type of animal: cat, dog, hamster, pig and zebra. Between them, they bred all five types. None bred an animal that sounded like their surname.

“Congratulations, Percy!” said Hogswill. I hear you have just won third prize in the pig-breeding competition!”

“That’s right,” said Zoe.

“And, Benjamin got second for dogs!”

“No,” said Benjamin. “You knows fine well I never touches no dogs. Not zebras, neither.”

Hogswill turned to the person whose surname sounded like the animals that Zoe bred. “And, did you win anything?”

“Yes, a gold medal for my prize hamster.”

Assuming  that all statements except the alleged second for dogs are true, who breeds what?”

More fun from Ian Stewart’s books is coming. Meanwhile, start sending your solutions!

Nalin Pithwa

### Strictly Logical

Only an elephant or a whale gives birth to a creature that weighs more than 100 kg.

The President weighs more than 150 kg.

Therefore, …

(Ref: Ian Stewart’s Cabinet of Mathematical Curiosities)

More fun on the way !!

Nalin Pithwa

### What Shape is a Crescent Moon?

The Moon is low in the sky shortly after sunset or before dawn; the bright part of its surface forms a beautiful creation. The two curves that form the boundary of the crescent resemble arcs of circles, and are often drawn that way. Assuming the Moon to be a perfect sphere, and the Sun’s rays to be parallel, are they arcs of circles?

Ref: Prof Ian Stewart’s Cabinet of Mathematical Curiosities.

More later,

Nalin Pithwa