April 2018 Brain Puzzler Solution

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

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