2016 AMC 10A Problems/Problem 9: Difference between revisions
No edit summary |
m Added 12A box |
||
| Line 11: | Line 11: | ||
==See Also== | ==See Also== | ||
{{AMC10 box|year=2016|ab=A|num-b=8|num-a=10}} | {{AMC10 box|year=2016|ab=A|num-b=8|num-a=10}} | ||
{{AMC12 box|year=2016|ab=A|num-b=5|num-a=7}} | |||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 11:59, 4 February 2016
Problem
A triangular array of 
coins has 
coin in the first row, 
coins in the second row, 
coins in the third row, and so on up to 
coins in the th row. What is the sum of the digits of ?
Solution
We are trying to find the value of such that ![\[1+2+3\cdots+N-1+N=\frac{N(N+1)}{2}=2016.\]](http://latex.artofproblemsolving.com/4/c/2/4c218461a24de88251f68d418e63eb0c6fdae6b8.png)
Noticing that 
we have 
so our answer is 
See Also
| 2016 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
| 2016 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 5 |
Followed by Problem 7 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
These problems are copyrighted © by the Mathematical Association of America. 
