Puzzle 68 - Reciprocals

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 The sum of two numbers is 10. The product of these numbers is 20. What is the sum of their reciprocals?

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Puzzle 15 : All but two

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Solution to puzzle 14 Huh, sending more money would have been much easier than this puzzle.      SEND     MORE   MONEY We have to find values for S,E,N,D,M,O,R,Y (8 digits out of 10).  Now, we're adding two 4-digits numbers.  Since 9999+9999 < 20000, M cannot be >=2. And by the "usual rules" for this kind of question, it can't be 0. So M=1 . Now, looking at the fourth (left-most) column, we have either S+1>=10 (if there's no carry) or 1+S+1>=10 (if there's carry). So S=8 or 9 , and O=0 or 1 . Since 1 is already taken, O=0   In the third column, we can't have E+0=N (no carry), so E+1=N and there's carry from the second column.   So in the second column either N+R=10+E=9+N, and R=9, or there's carry and 1+N+R=10+E=9+N, and R=8. So R=8 or 9 , just like S. IF S=8 and R=9,we're looking at 8END + 109E ====== 10NEY But this cannot possibly work: we need to get either E+0=10+N or 1+E+0=10+N i...
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Puzzle 128 - Kings and Queens

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