A woman had three old coins: a silver dollar, a quarter, and a dime. Each coin was a little battered and had a piece missing. She found that exactly the same fraction had broken away from each coin.
What fraction of each was missing if the value of the remaining bits of coins was now exactly one dollar in total?
For this puzzle it can be assumed that 1/2 a coin is worth 1/2 of its value.
Hint
This is a tricky question related to number bases.
Answer
200.
Each number in the sequence is a representation of the number 32 in different bases, starting with base 10.
Base 10: 32 = 3 x 10^1 + 2 x 10^0 = 3 x 10 + 2 = 32
Base 9 : 35 = 3 x 9^1 + 5 x 9^0 = 3 x 9 + 5 = 32
Base 8 : 40 = 4 x 8^1 + 0 x 8^0 = 4 x 8 + 0 = 32
Base 7 : 44 = 4 x 7^1 + 4 x 7^0 = 4 x 7 + 4 = 32
Base 6 : 52 = 5 x 6^1 + 2 x 6^0 = 5 x 6 + 2 = 32
Base 5 : 112 = 1 x 5^2 + 1 x 5^1 + 2 x 5^0 = 1 x 25 + 1 x 5 + 2 = 32
Base 4 : 200 = 2 x 4^2 + 0 x 4^1 + 0 x 4^0 = 2 x 16 + 0 + 0 = 32
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Puzzle 4
The same three-letter word has been removed from all of these words, leaving the letters below (which are still in the correct order).
