puzzles

Puzzles, Brain-Busters and Irritatingly Frustrating Teasers

Easy Ones:

Beginning with the word "STARTLING" remove a letter at a time such that at each stage the remaining letters in their order spell another word. Not a nonsensical word, but a real word. Until you are left with one letter, which still in itself is a word.
Farming neighbours Amy and Bessie went to market every day to sell their chickens. Bessie sold 30 chickens a day, at two chickens for $1.00, and brought home $15.00. Amy sold 30 chickens a day, at three chickens for $1.00, and brought home $10.00. One day Amy was sick, so she asked Bessie to sell her chickens for her. Bessie took the 60 chickens to market and sold them all at the rate of five chickens for $2.00. She brought home a total of $24 for the day's work. This was a dollar less than the two woman usually made each day when they sold their chickens seperately. What happened to the extra dollar? Did Bessie pocket it?
Along a similar vein is the "3 diners in the Restaurant" puzzle. Three men go to dine together in a restaurant. The bill comes to $25 and they each contribute $10. The waiter takes the money to the cashier, who gives the waiter the $5 in change. Being a non-assuming waiter he takes the change back to the three men. The men take back a dollar each, hence effectively paying $9.00 each, and they leave the $2.00 as a tip for the waiter. On their way out, one of them points out that they each paid $9.00 for the meal, amounting to $27.00, and the waiter was left with $2.00. What happened to the other remaining dollar? Did the cashier pocket it?
Who Dunnit? Allan, Brenda and Charles had so often expressed their opinion of Professor Popoff that when he was found murdered (stabbed to death with a dagger, but in a very refined way) it was natural that they would be suspected. In fact, for reasons that we don't need to go into now, it is certain that one of them is guilty. They made their statements as follows:
Looking back on the tragic event now, it is interesting to see that Allan and Brenda both made the same number of true statements. (This number can be anything from 0 to 3). Who killed Popoff?

Teasers

Who is or was Henry Squarepoint?
You are in a room with no windows to see through to orientate yourself, no metal objects on the door, roof, floor, walls or on your person other than two metal bars. Both these metal bars are identical other than that one of them is a permanent magnet and the other is just iron. You have a piece of string and nothing else to determine which is the permanent magnet and which is the iron bar. How would you do it?
How do you make 1 + 1 equal 41?
If magnets line up such that opposing poles attract, then why does a compass needle (or any suspended bar magnet) align such that its north pole faces the Earths magnetic north pole?

How "smart" are you?

There are various tests out there that purport to test your IQ, Intelligence Quotient. But unlike true IQ tests that are administered by qualified psychometricians, these are usually designed to flatter those better abled, rather than weed out those who need special education. There is naturally some degree of correlation and validity. But take that with a grain of salt too. Nevertheless, some of them contain some entertaining challenges and puzzles.

One of them is Wintelli. It runs on Win 3.x or higher, and you'll also need VBRUN300.DLL to run it. If you wish to take this seriously as an IQ test then you should find an hour of quiet time to do it. You may also be happy to know that this is almost exactly the same as Victor Serebriakoff's Test A in his book, Test Your IQ. The percentiles reported are percentage answers correct, and not which percentile of the population you fit into. The actual IQ score reported is pretty accurate IMO.

If the English language is a genuine problem for you, you could always take the "Culture Fair" test found at Euro Test. But be warned that it's norming is different in that a standard deviation with this test is about 23 IQ points as compared to Wintelli's 16 IQ points. So a score of 148 on the Euro Test is equivalent to 132 on Wintelli.

If you're good with these sort of questions, then you'll love the Mega Test found at Uncommonly Difficult I.Q. Tests. Also there for the masochist, is the Titan Test, and the Ultra Test. While you're there you may be interested to check out the norming tables.

More of these types of tests, including a whole battery of psychology and other fun tests reside at Barbarians Online Tests.

More Involved Puzzles

If you enjoyed some of the numerical and spatial puzzles of the type found in the Mega and Titan Tests, then you may like these too... You do not need a degree in mathematics to enjoy nutting out solutions to these. Just an avid interest to seek out the minimum necessary information required through any decent library.

Platonic Solids

Why are there only 5 Platonic Polyhedra in 3-D? How many regular Polytopes are there in higher Euclidean dimensions? Why?

Problema Bovinum

'If thou art diligent and wise, O stranger, compute the number of cattle of the Sun, who once upon a time grazed on the fields of the Thrinician isle of Sicily, divided into four herds of different colours, one milk white, another glossy black, the third yellow and the last dappled. In each herd were bulls, mighty in number according to these proportions: understand, stranger, that the white bulls were equal to a half and a third of the black together with the whole of the yellow, while the black were equal to the fourth part of the dappled and a fifth, together with, once more, the whole of the yellow. Observe further that the remaining bulls, the dappled, were equal to a sixth part of the white and a seventh, together with all the yellow. These were the proportions of the cows: the white were precisely equal to the third part and fourth of the whole herd of the black; while the black were equal to the fourth part once more of the dappled and with it a fifth part, when all, including the bulls, went to pasture together. Now the dappled in four parts were equal in number to a fifth part and a sixth of the yellow herd. Finally the yellow were in a number equal to the sixth part and seventh of the white herd. If thou canst accurately tell, O stranger, the number of the cattle of the Sun, giving separately the number of the well-fed bulls and again the number of females according to each colour, thou wouldst not be called unskilled or ignorant of numbers, but not yet shalt thou be numbered amongst the wise...

'But come, understand also all these conditions regarding the cows of the Sun. When the white bulls mingled their number with the black, they stood firm, equal in depth and breadth, and the plains of Thrinicia, stretching far in all ways, were filled with their multitude. Again, when the yellow and the dappled bulls were gathered into one herd they stood in such a manner that their number, beginning from one, grew slowly greater till it completed a triangular figure, there being no bulls of other colours in their midst nor none of them lacking.

'If thou art able, O stranger, to find out all these things and gather them together in your mind, giving all the relations, thou shalt depart crowned with glory and knowing that thou hast been adjudged perfect in this species of wisdom.'

Archimedes dedicated the above problem to his friend Eratosthenes. There are five solutions. The easiest to arrive at, apparently, has 206,545 digits, and begins with 776. I saw this number which filled 47 pages in 7 point in a journal of recreational mathematics. This is so many cows that if the cows were the size of electrons, they would overfill a sphere of radius greater than 30,000 light years! One of the other 4 solutions has apparently 5 million digits in it.

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