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If the candles are replaced each year, there are 66 candles; if you add the amount of candles on that year's cake to the ones you threw away last year, it will give you the answer. (Fraser)

I wrote down how many candles would be needed every birthday and used number bonds to get the answer 66. They are all triangular numbers: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66. (Lissa)