If you look at the earth as it is, the longitudes intersect the latitudes at 90o only at the equator. So the distance to be traversed will be either one-fourth the circumference of the earth or three-fourths the circumference of the earth.

Assuming that the earth is a perfect sphere, the same works with London as the pole. Using spherical trigonometry, the points B & C can be either of the following

Point B - at 26 deg 6' 18.591" N and 127 deg 56' 54.905" E, which would be a point in the island of Okinawa

and

Point C - at 26 deg 6' 18.591" N and 128 deg 9' 30.905" W, which would be a point south-west of Santa Barbara, California in the Pacific Ocean

OR

Point B - at 26 deg 6' 18.591" S and 52 deg 3' 5.095" W, which would be near Linha São Sebastião, Francisco Beltrão-PR, Paraná, Brazil

and

Point C - at 26 deg 6' 18.591" S and 51 deg 50' 29.095" E, which would be a point south-east of Madagascar in the Indian Ocean.

Venky

From some math or physics class or puzzle site we have all heard about the triangle with three right angles - because it is drawn on a sphere. Here it is again, but not so simply. From the question, we can in fact deduce that we have such a triangle. Let's call the first segment of the trip c (since it is opposite the angle at point C). The second segment, a, is defined as the same length as c. The law of sines for triangles on the sphere says sin(a)/sin(A) = sin(c)/sin(C),
so the angle of the trip at A (London) must also be a right angle.

Similarly, the segment of the trip from C to London must be the same length as the other two segments.

Now that that's out of the way, where are B and C? Let's start with the example three-right-angle triangle from all those homework questions, the one with one vertex at the north pole and the other two on the equator at 0 deg and 90 deg W. Since the Earth is a sphere (of course it isn't exactly, but I'm never going to solve this without assuming it is), we can slide that triangle around until one vertex is in London. That still leaves us one degree of freedom (i.e. it can be rotated around London) so we put one segment at a bearing of 45 deg from London.

We know the lengths of the segments are one quarter the circumference of the Earth (obvious from the initial triangle). This allows us to draw another triangle ABN, where N is the North Pole, and use the law of cosines on a sphere:

cos(a) = cos(b)cos(n)+sin(b)sin(n)cos(A)

In radians, n = c = pi/2 , A = pi/4 and b = (90-latitude_of_London)*pi/180 = 0.67195.
Since sin(n) = 1 and cos(n) = 0, cos(a) = sin(b)cos(A)
and a = 1.1487 radians = 65.82 deg. This puts B at latitude 24.18N.
A calculation for N (two solutions for inverse sine, pick the right one!) puts B at latitude 128.18E. Symmetry about the prime meridian (since the original bearing of 45 degrees bisects the 90 degree angle of the triangle at London) puts C at 24.18N, 128.18W.

We can double check the maths with the triangle BCN, we know b = c = 1.1487 (it was 'a' just a moment ago, but our angles have changed name) and angle N = 1.7738 (the longitude between B and C). This tells us that the length of the segment BC is indeed 90 degrees, give or take rounding errors, or one fourth the circumference of the Earth.

So in all, your trip has taken you over Scandinavia, Russia and China to point A off the east coast of Taiwan, over the Pacific to point B off the west coast of Mexico, and back over Mexico, the U.S., my house (go ahead, prove me wrong :-) ), and the North Atlantic home again.

Quite the personal transport you have, Martin!

Zack

Okinawa, Japan.

This is a somewhat ambiguous question, since "bearings" are quite different entities depending on whether you are dealing in Cartesian or spherical geometry. For this question, I will assume spherical geometry, where a "straight line" is the shortest distance across the sphere (i.e. a line following a "great circle", whose center is at the center of the earth) and a "bearing" is the initial compass direction defining the circle. This is a bit counterintuitive when thinking in two dimensions, since the compass bearing will typically change throughout the trip.

In order to meet the criteria of the given trip (two 90 degree turns that return you to your starting point) the distance traveled from point A to point B will be 1/4 the circumference of the earth (~10,000 km). To see why this is true, imagine the world tilted so that London is actually the North Pole. A trip on any bearing will proceed down a line of longitude (i.e. due South). After 10,000 km we would be at the equator, so a 90 degree left turn would send us east along the equator. (Note that longitude lines and the equator are all "great circles"). After 10,000km (1/4 of the way) around the equator, another left turn would send us due north again, back to the pole.

Now that we can visualize the trip, we need to do the same thing only from where London really is, and starting off at 45 degrees. Sparing you the math, a 10,000km great circle trip bearing at 45 degrees would take you around 26.40N 127.80E, which is on the island of Okinawa. You would arrive on a bearing of about 150 degrees, so a left turn would send you off again on a bearing of 60 degrees. Another 10,000km along this arc takes you to around 26.81N 127.90W, which is in the Pacific Ocean (between southern California and Hawaii). You would arrive on a bearing of 120 degrees. Another left turn would send you off at 30 degrees, which brings you back to London.

Pete Mitchell

The link is "-". Terry-Thomas on the left and Ann-Margret on the right. The hyphen is the link.

Venky

The photos are of actor Terry-Thomas [Thomas Terry Hoar Stevens] and singer/actress Ann-Margret [Ann-Margret Olsson], and the link is that both their screen names are made up of two first names connected with a hyphen.

Pete Mitchell

"Big Slick" (also "Santa Barbara" or a "Salt Lake Pair")

The reference is to poker, specifically "Texas Hold'em", where each player is dealt two cards which are then played along with up to five community cards. The first three community cards are turned over as a set and are called "the flop". The fourth card is "the turn". The final card is "the river".

"Snowmen" is slang for a pair of eights, which in this hand have lost when the "river" card was turned. A "cowboy" is a king and a "bullet" is an ace. Together, an A-K is sometimes called "Big Slick", though as with many combinations there are other slang terms as well including "Santa Barbara" or "a Salt Lake Pair".

Pete Mitchell

Bounce.

Ripe Cranberries: Dry, ripe cranberries bounce when they are dropped. John Webb, the first recorded New Jersey grower, was also the first person to notice that good cranberries bounce. Because he had a wooden leg, John couldn't carry his cranberries down the stairs, so he dropped them instead. He soon noticed that the firmest berries bounced to the bottom but the rotten ones stayed on the steps. Cranberries are therefore also known as bounceberries.

An ingenious twist to a deadly device: The Bouncing Bomb. For many years during World War II, all military leaders knew that if they could destroy the dams which gave power to the power stations, which in turn gave power to the munition factories. Then that country's war making machine capacity would be greatly slowed down. No bomber could attack these dams because a direct conventional bomb would almost certainly miss their target. It took the inventive genius of Barnes Wallis to come up with the design of a bomb which could bounce across the water to its target.

Barnes Wallis first began to think about producing a bouncing bomb in 1941. He was aware that in the 19th Century the British Navy had bounced cannon balls across the water to increase their range.

He began by carrying out experiments with glass marbles and a catapult on a tub of water in his back garden. He saw that given the correct angle and speed, the marbles would skim along the water without sinking. He then developed a prototype bouncing bomb at the National Physical Laboratory in Teddington. These tests were successful and the first prototype was dropped from an aircraft on Chesil Beach in December 1942.

In February 1943, Barnes Wallis was given the go ahead to prepare bouncing bombs for an attack on the Moehne and Eder Dams in the Ruhr. The Dambusters' raid took place on the 17th of May 1943 (Operation Downwood).

The cylindrical bombs were first spun to a speed of 500 rpm, and were dropped by the now famous 617 squadron at a height of 60 feet above the water of the dam, and at a speed of 240 mph. The rotating bombs skipped over the surface of the water and exploded while sinking to the base of the retaining walls of the dams.

The Dambuster bombing raids did indeed cause heavy damage to the dams which were targeted. The resulting flooding badly damaged German production in the Ruhr.

In using the Bouncing Bomb, the pilots of the 617 squadron had to fly very low and 7 of the 19 aircraft which took part in these raids were shot down by German anti aircraft guns.

Although the Bouncing Bomb worked, the RAF decided it could not sustain such heavy losses and the Bouncing Bomb was rarely used again during the war.

The economic activity of deceased felines: Dead Cat Bounces, which is market shorthand for short-lived share price rallies.

Venky.

The bat.
The agave plant - used to produce tequila - relies on bats for pollination and seed dispersal
The Bacardi brand has a bat as its logo
Whitby (North Yorkshire) is the setting for Bram Stoker's Dracula, whose connection with bats I need not elaborate
The famously paranoid quad biker, Ozzy Osbourne, will always be remembered for his on-stage exploits in Des Moines, Iowa, when in a wild moment he bit the head off a live bat thrown on stage by a fan, to the mixed horror and delight of the audience.

Venky

This one nearly drove me batty, yuk! yuk! Anyway:

long-nosed bats (Genus Leptonycteris) are the main pollinators of Century Plants (Agave sp.), and tequila is obtained through distillation of juices from agaves;

the Bacardi Company's corporate logo (and registered trademark) prominently features a bat;

Whitby was the setting of a significant portion (chapters 6-8) of the vampire novel Dracula, and its author Bram Stoker did much of his research there -- Dracula is able to shape-shift into, among other things, a bat;

the lead singer of the band Black Sabbath, whose best-known song is Paranoid, was Ozzy Osbourne, recently injured in a quad-bike crash, and famous for having reportedly bitten the head off a bat during a concert.

There are two ways of assigning the known professions to the players, but in either case Mr West's female partner is named Green and sits south at the white table.

See both solutions

Alan

Mr. West's partner is Dr. Green, and she sits south
at the white table.

Detailed logic and explanation. Numbers in parentheses
reference the known (or derived) facts that justify
each conclusion.

Given:

1. Each partnership is male/female, but never a couple.
2. Nobody sits at a direction or table that matches
their last name.
3. Neither Mr. and Mrs. West, nor the salesman and
his wife, sit at the same table.
4. A man sits north at each table.
5. The lawyer sits directly to his wife's right.
6. Mr. White is partner to the accountant's wife.
7. Mr. and Mrs. North sit in the same direction.
8. Dr. Green and the lawyer's wife do not sit in
the same direction.

Deductions:

9. The Whites sit at the green table and the Greens
sit at the white table (2).
10. The salesman is Mr. North, since it is a man (3) other
than Mr. West (3) and since the Greens and Whites
each sit at the same table (9) while the salesman and
his wife do not (3).
11. Mr. West and Mrs. North sit at one table while Mrs.
West and Mr. North sit at the other, since Mr. and
Mrs. West sit at different tables (3) and since there
must be the same number of men and women at each
table (1) and each table already has one couple (9).
12. Mr. White is partner to Mrs. West, since he must be
partner to either Mrs. West or Mrs. North (11,s1) but
Mrs. North is the salesman's wife (10) not the
accountant's wife (6).
13. Mr. West is the accountant (6,12).
14. Mr. White is the lawyer, since it must be a man (5)
who is not Mr. North (10) or Mr. West (13) or Mr.
Green (8*).
15. The Whites sit at the green table with Mr. North and
Mrs. West; the Greens sit at the white table with Mr.
West and Mrs. North (11,12).
16. Mr. White sits north at the green table, since a man
sits that direction (4) but it can't be Mr. North (2,15).
17. Mrs. White sits east at the green table (5,14); Mrs.
West, as Mr. White's partner (12), sits south; and Mr.
North sits west (the only seat left) (15).
18. Mrs. North sits west at the white table since she sits
the same direction as her husband (7,17).
19. Mr. West sits north at the white table since sitting
east would make the Green couple partners (1) and sitting
south would put a woman in the north seat (1,4).
20. Since the Greens must sit east and south at the white
table (15,18,19) and since Dr. Green does not sit east
(the same direction as Mrs. White, the lawyer's wife)
(8,14,17), it follows that Dr. Green must sit south at
the white table partnered with Mr. West (19), while
her husband, Mr. Green, sits east partnered with Mrs.
North.

* If Dr. Green is a man, then he can't also be the lawyer; if
Dr. Green is a woman then she can't be the lawyer's wife,
so Mr. Green can't be the lawyer.

Pete Mitchell

Johnny Hallyday, and the group Noir Desir. Rochez sur!

Alan

The French rock star, Johnny Hallyday (real name Jean-Philippe Smet) on the left. The French rock band Noir Désir on the right:-

From left Bertrand Cantat (lead singer), Frédéric Vidalenc (on bass), Denis Barthe (on drums) and Serge Teyssot-Gay (on guitar).

Venky

Johnny Hallyday (whoever the hell he is) and Noir Desir (whoever the
f**king hell they are).

Graybags

Between plait and pocket[-sized] you find plantain; plaster; plaudit; player; playwright; pleasure; plebeian; plethora; plumbago; plump; plunder; plus-fours; plutocrat; and poacher. And looking skywards, the planets, including Pluto, and the Pleiades.

Alan

Austin Powers.

The clues refer to people whose first names are also U.S. state
capitals, as follows:

Olympia Dukakis, actress, whose cousin Michael Dukakis was the
former governor of Massachusetts and Democratic candidate for
the U.S. Presidency in 1988 (losing to George Bush, senior).
Olympia is the capital of Washington.

Jackson Pollack, abstract impressionist painter. Jackson is the
capital of Mississippi.

Pierre Trudeau, Prime Minister of Canada from 1968 to 1979 and
again from 1980 to 1984. Pierre is the capital of South Dakota.

Helena Bonham Carter plays Amanda, wife to Woody Allen's Lenny,
in the 1995 film "Mighty Aphrodite". Helena is the capital of
Montana.

Lady Augusta Bracknell is Gwendolyn's mother in "The Importance of
Being Earnest". Augusta is the capital of Maine.

The spy, therefore, is Austin Powers, Austin being the capital of
Texas.

Pete Mitchell

Q1

Q2

Q3

Q4

Q5

Q6

Q7

Q8

Q9

Q10

Pete Mitchell

9

Alan

9

Zack

8

Venky

8

Graybags

7

Neal

5