Difference between revisions of "2012 UNCO Math Contest II Problems/Problem 9"
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== Solution == | == Solution == | ||
| − | + | (a) <math>{N-1}2^{N+1}+2</math> (b) <math>2201</math> | |
== See Also == | == See Also == | ||
Latest revision as of 02:26, 13 January 2019
Problem
Treasure Chest . You have a long row of boxes. The 1st box contains no coin. The next
boxes each contain 
coin. The next 
boxes each contain coins. The next 
boxes each
contain 
coins. And so on, so that there are 
boxes containing exactly 
coins.
(a) If you combine the coins from all the boxes that contain 
, or coins you get 
coins. How many coins do you get when you combine the coins from all the boxes that
contain 
or coins? Give a closed formula in terms of . That is, give a
formula that does not use ellipsis 
or summation notation.
(b) Combine the coins from the first 
boxes. What is the smallest value of for which
the total number of coins exceeds 
? (Remember to count the first box.)
Solution
(a) 
(b) 
See Also
| 2012 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNCO Math Contest Problems and Solutions | ||
