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ONE OF the attractions of the rubber-band trick featured last week is that it is all in the fingers. You can't go wrong. (See the diagram if you haven't worked it out yet.)

Not like the digits puzzle quoted in this column on 21 November. There, the idea was to correct the following "sum" by rearrangement only: 123 x 456 = 78.

Isn't it odd how there isn't a strictly correct word for "sum" to describe a simple calculation involving operations other than just additions? But I digress. So relieved was I at finding any solution at all that I lazily assumed it was a unique one.

Rosie Forth of Colchester wrote to point out that besides the proffered solution of 3 x 582 = 1,746, there was also 6 x 453 = 2,718, 57 x 24 = 1,368, 64 x 58 = 3,712 and 34 x 52 = 1,768.

Of course, Ms Forth does not have to list all the solutions to prove my solution incomplete, which is a pity as I could then have pointed out that her list of solutions is also incomplete; 37 x 58 = 2,146 and 3 x 582 = 1,746, for example, are missing. Does it stop there? I doubt it.

Indeed, it has been suggested that I deliberately introduce mistakes into my work in order to encourage correspondence. In my experience, mistakes don't have to be introduced. They happen on their own.

I once set a spelling puzzle in the now-defunct Early Times. It was the sort of thing where you had to state which of a list of words had been misspelt. One of the sub-editors, reading for words and not for sense, corrected all the spellings in the list, though he curiously misspelt misspelt as mispelt.

This sort of thing happens a lot, fostering a belief in gremlins among the spiritual and so'd law among materialosts.

An illustrator friend cites instances where instructions accompanying drawings such as "Reduce" or "This Way Up" have been kept in the picture.

Nevertheless, without the opportunity to make mistakes we could not learn. What is the case is often best defined by its boundary with what is not the case. My neuropsychologist friend, Dr Baxter, tells me that in social-skills training it is extremely useful to get clients to act out scenarios badly so that mistakes can be identified and analysed. There is never any shortage of volunteers.

I'm not saying that some mistakes aren't serious. But not all mistakes are bad as the conventional examples of Fleming, Columbus and Goodyear demonstrate. Indeed, the whole point of learning through play is to explore and indulge one's native curiosity in an environment in which mistakes do not matter. You have to survive something to learn from it. What distinguishes the creative person who survives a mistake is the use made of it.

Only fools never make mistakes. Was it not Doctor Johnson who, on being asked by a lady how it was that he came to define pastern as the knee of a horse, replied forthrightly: "Ignorance, madam, pure ignorance"?

Even Jeremy Paxman doesn't always get it spot on. On University Challenge recently, he asked what was special about the Fahrenheit equivalents of 16C and 28C. The answer? They are the reversal of the Celsius figures: ie that 16C was 61F and 28C was 82F. Not so, though it is easy to see how the setter arrived at this inexactitude: temperatures quoted in weather forecasts are always rounded up to the nearest whole number.

Nor is it just when people stray into other fields that mistakes occur. "The A-Z of English" on BBC2's The Learning Zone the other night covered topics as varied as accent and Franglais, surefootedly steering clear of anything un-PC. As several linguistic devices were listed, there appeared the word diphthong - but spelt dipthong without the "h".

Mistakes - like accidents - will happen. In fact I often think that where a mistake appears not to have happened it is only because two mistakes have cancelled each other out. Then again, I could be wrong.

Points to ponder:

1. Correct this "sum" in the laziest way possible: 16 x 6 = 618.

2. Which author almost named his book The Chronic Argonauts?

3. What is a pastern?

4. What is 28C in Fahrenheit?

Solution to Didcot Broadway Puzzle:

Only bulbs whose ordinal number has an odd number of factors will end up on. Only square numbers have an odd number of factors. So bulbs 1, 4, 9, 16... end up lit. There were 109 bulbs in total (there are 10 square numbers less than 109).