1st Swedish 1961 Problem 3 For which n is it possible to put n identical candles in a candlestick and to light them as follows. For i = 1, 2, ... , n, exactly i candles are lit on day i and burn for exactly one hour. At the end of day n, all n candles must be burnt out. State a possible rule for deciding which candles to light on day i.
n odd. If i  n/2, light i candles starting from n. Eg 1; 1,2; 3,4,5; 2,3,4,5; 1,2,3,4,5. Solution Total candle hours = 1 + 2 + ... + n = n(n+1)/2. Hence (n+1)/2 per candle. But each candle is lit for a whole number of hours, so n must be odd. Rule above gives pairs of days 1, 2, ... , i and i+1, i+2, ... , n, plus the final day when all candles are lit. Each candle is lit once for each pair of days (and is lit on the final day). 1st Swedish 1961 © John Scholes jscholes@kalva.demon.co.uk 30 December 2003 Last corrected/updated 30 Dec 03