Birthday Candles
Since he was 40 years old, Grandpa Edward has celebrated all of his birthdays by using candles shaped in the digits from 0 to 9 to indicate his age. First, he bought the candles of numbers 0 and 4. He always kept the candles to use in future birthdays, and only bought a new candle when it was not possible to indicate his age with the current candles. For example, when he was 41, he bought the candle of number 1.
Today, Grandpa Edward is 85 years old. How many candles has he had to buy, to light up his birthday cake throughout the years?
Include the candles of numbers 4 and 0 in your count.
Image credit: Wikipedia Gustavo86 .
The answer is 14.
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5 solutions
First, note that the units digit goes through all 0 → 9 digits, so our answer is at least 1 0 . However, we see that 4 4 → 7 7 requires the use of more than one digit, namely 4 → 7 . We need 4 extra digits, bringing the number of candles bought up to 1 4 .