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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Comments
OK... First of all how does this fall under the topic Letter-Equations? This should have been a Math brain teaser. Secondly, this teaser was not posed properly. It would have been clearer if you had said what were the 4 smallest coefficients in the "EXPANSION" of (x + y) ^123456789 and not the "expression". There is a difference in these words!!! From there it would have been clear to anyone with a mathematical background that you are referring to the binomial expansion of (x + y) ^ 123456789. Also to correct you the method used to determine the coefficients is not called the Fibonacci triangle but it is called the Pascal triangle.
i dunt understand - even a lil bit.. it confused me.. i think the question is 'search the valu of x and y'.. really confusing
I t would have been more fun if it wasnt do darn hard for me...
(so) ^
Pretty easy but clever.
However, I do agree with all of the comments by mercenery007. I see that the teaser has been moved to to the math category at least.
However, I do agree with all of the comments by mercenery007. I see that the teaser has been moved to to the math category at least.
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