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…

Q: Sabina’s car has 50% better fuel efficiency (miles per gallon) than her old car.  The new car uses diesel which is 20% more costly than the gas in her old car.  On a percent basis, how much will she save on a long trip?

A:  20%
For this problem, we made up numbers to make the Math easier :)
We can use 10 miles per gallon for Sabina’s old car which would make the new one 15 mpg.
We can pick an easy number that plays nice with 10 and 15 like 30.
If she goes 30 miles on a trip, she will need 3 gallons with the old car but only 2 gallons with the new car.
Now we need a price for gas so we assumed $4.
If gas is $4/gallon but diesel is 20% more at $4.80 per gallon, she would have spent 3 x $4 = $12 with the old car but now spends only $9.60 for the new car (2 x $4.80).
She saved $2.40 on $12 which is a 20% savings.

Q: How many 6 digit numbers are there whose digits sum to 51?

A: 56.

There are 3 possible sets of 6 numbers: 999996 where the 6 can be the 1st, 2nd, 3rd, 4th, 5th, 6th place values making 6 6 digit numbers

3 9s and 3 8s which is the same probability as 3 boys and 3 girls with 6 children 3C6 = 20 6 digit numbers

and 4 9s with an 8 and a 7 with 30 possibilities
789999
798999
799899
799989
799998
879999
897999
899799
899979
899997
978999
979899
979989
979998
987999
989799
989979
989997
997899
997989
997998
998799
998979
998997
999789
999798
999879
999897
999978
999987

credit to Julia Robinson Mathematics Festival