Brain Teasers
Efficient Coefficients
The sum of the four smallest coefficients in the expression
(x+y)^123456789
is a nine-digit number with each digit being a distinct number from the following set of numbers:
1,2,3,4,5,6,7,8,9,0
What number from the set does not appear as a digit in the sum?
(x+y)^123456789
is a nine-digit number with each digit being a distinct number from the following set of numbers:
1,2,3,4,5,6,7,8,9,0
What number from the set does not appear as a digit in the sum?
Answer
7According to the Pascal triangle, the two coefficients at either end of of the expression (x+y)^z will be 1,1,z, and z. Therefore, the sum of the four smallest coefficients is
1+1+123456789+123456789=246913580
The digit 7 is absent from this sum.
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