Hugh Apsimon, Author at New �Ӱ�ԭ��

Enigma 880 : Let there be light

Hugh Apsimon — Fri, 21 Jun 1996 23:00:00 +0000

The floor and the four walls of Tom’s optical laboratory are each
rectangular, and each is covered in non-reflective material. The ceiling, too,
is rectangular—but is a perfectly reflecting mirror. Within the room there
is a specific fixed point—the “object-point”—at which minuscule
objects may be placed for examination: the object-point is 8 foot 1 inch below
the nearest point of the ceiling. In the room there is also a fixed vertical
rod, from floor to ceiling: it meets the ceiling at a point distant 14 foot 1
inch from the object-point. On this rod there is mounted a point-source of light
(of equal illuminative intensity in all directions): this point-source can be
freely moved up and down the rod, but can not be moved in any other direction.
This point-source is the sole source of illumination in the room.

In order to have the greatest total illumination at the object-point, how far
from the top of the rod should Tom station the point-source?

A £10 book token will be awarded to the sender of the first correct
answer opened on Thursday 25 July. The Editor’s decision is final. Please send
entries to Enigma 880, New �Ӱ�ԭ��, King’s Reach Tower, Stamford Street,
London SE99 0BB. The winner of Enigma 874 was Stephanie Clarke of Thane,
Oxfordshire.

Answer to Enigma 874

Scamelot lottery

11, 19, 23, 31, 41 and 43.

Tomorrow and tomorrow

Hugh Apsimon — Sat, 10 Feb 1996 00:00:00 +0000

ENIGMA 861

TOM, Dick, Harry, Anne and Belinda are on holiday together on the island of Alvbe [Ars Longa Vita Brevis Est], where it is the custom to celebrate diversaries [rather than anniversaries] of everything – and particularly of one’s birth.

Today Tom is celebrating a palindromic diversary of his birth. “Happy prime diversary”, says Anne. “And tomorrow you’ll be twice a prime,” says Dick. “And the day after tomorrow you’ll be three times a prime,” says Belinda. “And the day after that you’ll be four times a prime,” says Harry.

So, how old is Tom today (in, of course, days – the number of days since his birth)?

A £10 book token will be awarded to the sender of the first correct answer opened on Thursday 14 March. The Editor’s decision is final. Please send entries to Enigma 861, New �Ӱ�ԭ��, King’s Reach Tower, Stamford Street, London SE99 0BB. The winner of Enigma 854 was D. Vincent of Watford, Herts. and the winner of Enigma 855 was Charles Pochin of Havant, Hants.

Answer to Enigmas

854 and 855

Colourful Christmas and Magic moment

854: They can produce (ii) but not (i) and (iii).

855: 25 February.

ENIGMA: No.848 Not-so-ambiguous clock

Hugh Apsimon — Sat, 11 Nov 1995 00:00:00 +0000

BELINDA’S birthday present from Anne was a clock. It’s a very accurate clock, and one whose hands point, at any given time, exactly where they should point at that time. But the clock does have one drawback: by some whim of fashion its minute and hour hands are identical in appearance.

Belinda telephoned Anne: “It’s lovely – but it’s stopped. And however accurately I measure the position of its hour hand and its minute hand, I can’t find out when it stopped because I don’t know which hand is which. It’s one of two possible times, quite a bit apart; but I can’t tell which.

Anne: “And just where is its second hand pointing?”

Belinda: “I hadn’t thought of that … Almost straight up: it would have been pointing straight up less than half a second after the clock stopped – if the clock hadn’t stopped (if you see what I mean).”

Anne: “Well then, if the clock had been able to go on for that ‘less than half a second’, and had then stopped with its second hand pointing straight up, it would have stopped when the time was H hours and M minutes.”

What are the whole numbers H and M?

A £10 book token will be awarded to the sender of the first correct answer opened on Thursday 14 December. The Editor’s decision is final. Please send entries to Enigma 848, New �Ӱ�ԭ��, King’s Reach Tower, Stamford Street, London SE99 0BB. The winner of Enigma 842 was Anna Brady of Herne Hill, London.

Answer to Enigma 842

Cover photo

(i) Yes; (ii) X; (iii) “One point is exactly covered by its photographic image”.