August 2018 Brain Puzzler Solution

Q: If you only have 4s and 5s to make other numbers (such as 4 + 4 + 5 = 13 and 5 + 5 + 5 + 5 + 5 = 25),  how many numbers from 1 to 1000 have this property ?

A: 994
Which #s cannot be made?  There are 6 numbers that cannot be made:1 2 3 6 7  or 11.
That leaves 994 numbers.
All others can be made from 4s and 5s as 8 is 2 4s and 9 is 4 and 5 and 10 is 5 and 5.
After 12 which is 3 x 4, all other numbers can be made.
See above for 13, 14 is 9+5, 15 is 3 5s, 16 is 4 4 s 17 is 12 +5, 18 is 14 + 4, 19 is 15 +4 and so on and so on…

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