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Floor Equation (Posted on 2014-12-02) Difficulty: 3 of 5
M is a real number satisfying this equation:

floor(M + 19/100) + floor(M + 20/100) + ....+ floor(M + 91/100) = 546

Find floor(100*M).

No Solution Yet Submitted by K Sengupta    
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Solution solution Comment 2 of 2 |
There are 73 terms adding up to 546, so the average of the terms is 7+35/73.

That is, if each term were 7, the total would be 511. We need 35 more, so 35 of the terms should be pushed above 7: those with the highest 35 fractions, starting at 57/100.

For 7 + f + 57/100 to be 8 or above requires that f be at least 43/100.

For 7 + f + 56/100 to be less than 8 requires that f be less than 44/100.

7 + 43/100 <= M < 7 + 44/100.

floor(100*M) = 743.

  Posted by Charlie on 2014-12-02 14:02:29
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