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Some of these and some of those (Posted on 2018-04-30) Difficulty: 2 of 5
One day on the board, Ms. Math wrote the digits 1 to 9. She then wrote a certain number of fives and also a number of eights. The number of fives and the number of eights were not necessarily the same. The mean (average) of all the digits on the board is 6.4.

Determine the smallest number of digits that can be on the board

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution my KISS solution Comment 2 of 2 |
Since the average is 6.4 the total must be divisible by 32.
So we have to find number of fives (f) and number of eights (e)
satisfying the equation  5f+8e= 32k-45.
Trying to solve for k=2,3,   ... etc  and checking  the integer solutions to fit the average  TOTAL / (F+E) =6.4  we are ok when k=6:
  e=4 or 9 or 14,   but only 14 provides the correct average.
ANSWER: 14 EIGHTS  + 7 FIVES  + (9 original digits) sum up to 112+35+45=192     
192: (14+7+9)=192/30=6.4

Edited on April 30, 2018, 6:47 pm
  Posted by Ady TZIDON on 2018-04-30 18:43:27

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