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I WAS running through the solution to last week's rope puzzle with pTom. (His name's Tom really, but somehow he got rechristened pTom, the p being silent as in a broken whistle. His little brother calls me Twis, so there's a sort of overall justice to it.)

To get disentangled (see diagram), take a loop of the string connecting your wrists and push it under the bit encircling one of your companion's wrists. Then hook it over his hand and you will find yourselves as separately bound as the volumes of the Shorter English Dictionary.

"Tell me all you know about rubber bands," I asked my helper as we discarded the string. "Why is my friend Baxter's garden path littered with elastic bands, while her neighbour's isn't?"

"Maybe the postman has something against her," ventured pTom.

"Not the postman," I said, sensing an opportunity. "Though the window cleaner has something against her house."

"What?" asked pTom, walking into the trap.

"A ladder," I replied. pTom blinked reproachfully...

How functional and versatile rubber bands are. They are not just for securing the tops on jars of home-made jam or lids on lunchboxes. They are the poor person's bicycle clip and arm band. You can use them to keep your socks up, to tie your hair in pigtails if you don't mind split ends, or to attach a label to a suitcase without tying a knot.

And when I tripped on an uneven pavement the other day so that the sole of my right shoe began to flap ominously, what saved the day? A grubby little rubber band found amid the clutter in my coat pocket. Wrapped around the instep it saw me back to base camp and a change of shoes.

Have Goodness & Mercy followed me all my days? I'm not sure. But rubber bands I can vouch for. They've always been there for me. My days have been measured out in them. At school in the days of short trousers you would use a laggy band to flick the legs of the chap in front or to propel bits of paper from the back of the class to the front, feigning innocence when the teacher looked around from the scrawl on the blackboard.

A twisted band provided the motive power for balsa airplanes. These were of two kinds. The ones on which you laboured for days cutting out ribs and struts, and assembling them into a rickety framework which you covered with tissue, doped and painted. Your model Spitfire would generally prang, if not on its maiden flight, then soon after.

The prefab variety made no pretence at realism. Its sheet-balsa wings and tailplane were attached to a stick fuselage underslung with a rubber band, anchored at one end to a hook and at the other to the shaft of the propellor.

The wings were always the first to go, because they stuck out so much. But the intact fuselage, tail section and propulsion system could be lowered nose-first into the rainwater barrel, where it would wind its slow way down through the Stygian gloom to the bottom, where it could be heard sluggishly churning up the sediment before bobbing back up again a few minutes later.

In this inverted anti-world the propellor of the lighter-than-water craft turned visibly slowly and the "flight" time was extended from seconds to minutes. Of course, you only saw your Vertical Submersible, Bottom- Scouring, Eventually Resurfacing and Sadly Non-Acronymic Unit at the beginning and end of missions, but this only made it more exciting, like one of those marriages that thrive on separation.

Perhaps because this voyage to the bottom of the barrel was an act of the imagination it seemed more engaging than flying the airplane it had started from.

It was the new improved model. Now without wings.

Points to Ponder

1. How can you verify that a rain barrel is exactly half full of water? (You are to imagine no measuring sticks or strings are available.)

2. What is the final digit of 7 raised to the 999th power?

Solutions from last week

Q4. Successive powers of 6 (and of any number ending in 6) end in 6. So 666 to the 999th power ends in 6. 9 (and any number ending in 9) raised to an odd power ends in 9 and raised to an even power ends in 1. So 999 to the 666th ends in 1. The sum of the two numbers ends in 7 and so is not divisible by 5 without remainder.

Q5. To make two sevens into two thousand, write the sevens as VII (eg with matches) and rearrange them to make MM.