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I HAVE just bought a new electronic clock and I have to put in the fraction of a second which elapses between updates of the clock’s display. For example if I put in 8/13 then the clock’s display will update at the following times after I start the clock:

The clock’s display actually gives the time to the nearest second and so in this case it shows, in turn:

1,1,2,2,3,4,4,5,5, …

I can put in any fraction I choose, provided that the denominator is odd.

For each of the following sequences, say whether or not I can put in a fraction so that the clock’s sequence of displays begins with the given sequence:

(a) 1,2,3,4,5,5,6,6 .

(b) 1,2,3,4,4,5,6,7,8,8 .

(c) 1,2,3,4,4,5,6,7,8,9,10,11,12,13,13.

(d) 1,2,3,4,4,5,6,7,8,9,10,11,12,13,14.

A £10 book token will be awarded to the sender of the first correct answer opened on Thursday 4th April. The Editor’s decision is final. Please send entries to Enigma 864, New Å®ÉúСÊÓƵ, King’s Reach Tower, Stamford Street, London SE99 0BB. The winner of Enigma 858 was John Hobley of Como, Western Australia.

Answer to Enigma 858

A matter of degree

156° and 62°F .