Number game
Reading car number plates in a long, dreary queue one day, I noticed if you take any three-digit number, reverse the digits then subtract the smaller from the larger, the answer is always divisible by 9. For example, 761 鈭� 167 = 594, and 594 梅 9 = 66. This obviously doesn鈥檛 work for symmetrical numbers such as 555 or 919 but, in other cases, how and why does it happen?
鈥� A three-digit number, abc, can be written 100a + 10b + c. When reversed, this number has c in the hundreds column, b in the tens column and a in the units column: 100c + 10b + a.
The next stage is to take one number from the other, grouping multiples of a, b and c.
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(100a + 10b + 1c) 鈭� (100c + 10b + 1a) = (100 鈭� 1)a + (10 鈭� 10)b + (1 鈭� 100)c
The answer is 99a + 0b 鈭� 99c.
If a and c are the same you end up with zero. If a and c are different the answer is always something multiplied by 99. Therefore, this is not only divisible by 9, but is also divisible by 11.
Eleanor Loukes
Seal Chart, Kent, UK
Growth areas
My doctor tells me that the fungus that causes athlete鈥檚 foot tends to occur between the third and fourth toes. What is it about this area that the fungus prefers and how does this site differ from the space between all the other toes?
鈥� Sadly, I am one of those unfortunate people who suffers from recurrent athlete鈥檚 foot only between my third and fourth toes. All my other toes have a clear gap between them at their bases, but my third and fourth toes adjoin closely. This reduces the evaporation of moisture from this site, which in turn creates a welcoming environment for fungus 鈥� especially when I wear the same socks for 36 hours. Sorry, but this has been known when I have had to work all night on call.
In fact, I now prevent the return of athlete鈥檚 foot by placing cotton balls or gauze between my third and fourth toes. This helps keep the area dry and is much cheaper than anti-fungal creams. Despite my having a medical doctorate and a PhD from Johns Hopkins University, my wife thinks that this treatment is half-baked.
John Criscione
Department of Biomedical Engineering
Texas A&M University, College Station, US
鈥� The organism responsible for tinea (better known as ringworm), or athlete鈥檚 foot, does not have an intelligent territorial instinct that leads it to a predestined home. Infections by the fungus responsible, Trichophyton mentagrophytes, begin in the space between the third and fourth toes because this location offers the ideal environment of a warm, dark and moist collection of dead skin cells.
The outer edges of the human foot are relatively flexible, having joints capable of motion in three planes. The spaces between all the other toes are therefore subject to a greater diversity of movement and forces, providing ventilation and the opportunity to slough off dead skin cells. Meanwhile, in the dark recesses between the less mobile third and fourth toes, a virtual agar plate awaits the arrival of T. mentagrophytes.
Felicity Prentice, Melbourne, Australia
Unshockable:
My science class would like to know why an electric eel does not shock itself when attacking its prey.
鈥� A number of fish are able to generate electric fields using modified striated muscle fibres. These are made of stacks of flattened cells that add together the small electrical potentials of each cell, like a number of batteries wired in series, giving rise to a much larger voltage. In a few species, such as the marine ray, electric eel and catfish, the voltage generated is sufficient to stun prey.
In the case of the electric eel, the striated muscle fibres are found along its tail. When the eel contracts these muscle fibres, the resulting current does indeed flow through its tail, but because the muscles are contracted there is little effect on the eel itself. You can demonstrate this yourself if you give yourself an electric shock from static electricity, for example when touching a car door handle. You can minimise the shock by clenching your fist and touching the handle first with your knuckle. You will see and hear the spark but feel very little.
The electric eel is particularly dangerous because it can generate a potential of up to 500 volts, which is sufficient to stun a human and cause death by drowning. Because the head of the eel is outside the main current flow it seems able to withstand damage to its own nervous system. However, it has been reported that older eels suffer blindness and this may be a side effect of experiencing many electric shocks.
Many other fish are also able to generate low-voltage electric fields, which they use for electrolocation and prey detection, and possibly for species recognition and signalling.
Peter Rigby
Winchburgh, West Lothian, UK
This week鈥檚 questions
Environmental controls
On a roundabout just off the M25 motorway near London, there are signs labelled 鈥淧ollution Control Valve鈥�. What is this? And, if it鈥檚 not a facetious question, where does the pollution go when the valve is shut?
Pete Edwards
Cambridge, UK
Boring method
In the 1 March edition of 鈥淭he Last Word鈥�, Syd Curtis asks a question about how to make ice, saying he got the recipe from the Windsor Recipe Book. In passing, he also mentioned the book had a recipe for 鈥渉ow to bore holes in glass using camphor dissolved in turpentine鈥�. Does this method really work, and if so, what are the details?
Jonathan Cohen
No address supplied