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For reference, we number the seven bars in the reverse-S pattern

shown. We can then refer to a pattern by its binary 7-tuple or its decimal equivalent. E.g. the number one is displayed by having bars 3 and 7 on, which gives a binary pattern 1000100 corresponding to decimal 68. NOTE that there is some ambiguity with the 6 / 9. Most versions use the upper / lower bar for these, i.e. 1101111 / 1111011, but the bar is sometimes omitted, giving 1001111 / 1111001. I will assume the first case unless specified.

I have been interested in these for some time for several reasons. First, my wife has such a clock on her side of the bed and she often has a glass of water in front of it, causing patterns to be reversed. At other times the clock has been on the floor upside down, causing a different reversal of patterns. Second, segments often fail or get stuck on and I have tried to analyse which would be the worst segment to fail or get stuck. As an example, the clock in my previous car went from 16:59 to 15:00. Third, I have analysed which segment(s) in a clock are used most/least often.

Birtwistle. Calculator Puzzle Book. 1978. Prob. 35: New numbers, pp. 26-27 & 83. Asks for the number of new digits one can make, subject to their being connected and full height. Says it is difficult to determine when these are distinct -- e.g. calculators differ as to the form of their 6s and 9s -- so he is not sure how to count, but he gives 22 examples. I find there are 55 connected, full-height patterns.

Gordon Alabaster, proposer & Robert Hill, solver. Problem 134.3 -- Clock watching. M500 134 (Aug 1993) 17 & 135 (Oct 1993) 14-15. Proposer notes that one segment of the units digit of the seconds on his station clock was stuck on, but that the sequence of symbols produced were all proper digits. Which segment was stuck? Asks if there are answers for 2, ..., 6 segments stuck on. Solver gives systematic tables and discusses problems of how to determine which segment(s) are stuck and whether one can deduce the correct time when the stuck segments are known.

Martin Watson. Email to NOBNET, 17 Apr 2000 08:17:32 PDT [NOBNET 2334]. Observes that the 10 digits have a total of 49 segments and asks if they can be placed on a 4 x 5 square grid. He calls these forms 'digigrams'. He had been unable to find a solution but Leonard Campbell has found 5 distinct solutions, though they do no differ greatly. He has the pieces and some discussion on his website: http://martnal.tripod.com/puzzles.html . Dario Uri [22 Apr 2000 14:44:35 +0200] found two extra solutions, but Rick Eason [22 Apr 2000 09:37: -0400] also found these, but points out that these have an error due to misreading the lattice which gives the two bars of the 1 being parallel instead of end to end. Eason's program also found the 5 solutions.