1) What is the quickest way of filling three cups from an automatic coffee dispenser with two spouts?
And Rob Eastaway who asked:
2) Why does 47 turn up so often as a factor of the total cost when buying computer hardware?
I shall also miss Professor David Singmaster's disrupting the peace of the Langham Hotel tea-room as some puzzle-toy exploded out of his bulging rucksack or as he posed artlessly, his head jammed inside a truncated icosahedron to illustrate some point about the best design of footballs.
I shall remember also the day I insisted we get more women on the panel. After days of doggedly pursuing one Susan Denham who wrote puzzles for New Scientist, Harry Parker, the producer, finally discovered that Sue Denham was the pseudonym (geddit?) of Dr Victor Bryant, a fun-loving mathematician indeed - but a man.
What makes a puzzle easy or difficult to process is a psychological matter. Take for example the puzzles set by Dr. Doreen Baxter, consultant neuropsychologist at the Kemsley Brain Injury Unit, Northampton:
3) Find a simple word in which OE rhymes with BOO.
4) Find a word in which OO is pronounced like the O in GO.
These illustrations of the vagaries of English throw light on how the brain stores and retrieves what we read. This in turn gives an insight into how to help individuals who have suffered damage through strokes or car crashes. Dr Baxter, after all, mostly spends her time solving real and serious problems.
Puzzle-setting is a secretive and lonely pursuit, and solitary solving gives a buzz of IQ realised. A co-operatively sportive and supportive team, on the other hand affords the extra buzz of shared exploration.
Not all panellists turned out to be team-players, of course, but my experience suggests that they all could be made so if only their insecurities could be overcome. Puzzles as therapy; whatever next?
Mind you, I thought I'd need therapy when I saw the mountain of correspondence generated by The Puzzle of The Three Singmasters:
4) On entering Broadcasting House, I find not one, but three Singmasters. I know that one always lies, one always tells the truth and the other alternates. What is the most elegant way of identifying the truthful one?
This opened not just a can, but a diet of worms. In Room 7058 the producer Harry Parker and I waded through a swamp of e-mails, letters and faxes. My attempts to understand all the different, and highly individualistic proofs sent in by listeners drove me to long consultation with logicians and philosophers, who patiently explained the distinction between opposite, contrary and subcontrary and soon convinced me that telling the truth was simple, but the concept of lying was anything but straightforward.
I was delighted, however, that such a short question could generate enough heat to last well into winter. And that I was instrumental in inspiring puzzles such as this neat one propounded by David Broughton:
5) In how many different ways can you make a cup of tea?
To abstract the essentials, as Dr Baxter would say, there are six subtasks: C (get Cup from Cupboard), B (Boil water), I (Infuse tea in pot), M (Milk into cup), T (pour Tea) and S (Sugar in cup). You can't do I until you've done B, and you can't do T until you've done I. Then again you can't do M, T or S until you've done C. So how many ways are there of doing it? Well?
1. Start filling cups A & B. When both are half full, replace B by C. When A is full replace it by B which is half full. That way both nozzles are always occupied in filling.
2. VAT at 17.5 per cent means multiplying pre-tax prices by 117.5 = 47 x 2.5. So any even number of pounds is divisible by 47 when tax is included. Eg pounds 22 x 117.5 = pounds 25.85 after tax, which equals 55p x 47.
3. SHOE, CANOE, or (less simple) HOOPOE.
5. eg Ask any one of the trio:
"If my next question but one to you is `Which of your colleagues is the truth-teller?' which one do you indicate?" The truth-teller either cannot answer or must say "neither". Both liar and alternator must indicate the truth-teller.
6. Thirty-eight ways.Reuse content