Difference between revisions of "2013 UNCO Math Contest II Problems/Problem 5"
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<math>2+3+4+4+4</math>, etc., which have repeated terms. You need not justify your answer on this question. | <math>2+3+4+4+4</math>, etc., which have repeated terms. You need not justify your answer on this question. | ||
| − | <math>\begin{ | + | <math>\begin{array}{|c|c|c|c|} |
\hline | \hline | ||
| − | EXAMPLE: & Distinct Integers: {2, 3, 4, 8} & Their Sum: 2+3+4+8=17 & Their Product: 2 \times 3\times 4\times 8=192 \\ | + | \text{EXAMPLE: }& \text{Distinct Integers: }{2, 3, 4, 8} & \text{Their Sum: }2+3+4+8=17 & \text{Their Product: }2 \times 3\times 4\times 8=192 \\ |
\hline | \hline | ||
| − | \end{ | + | \end{array}</math> |
| − | |||
| − | |||
== Solution == | == Solution == | ||
| + | Intuitively, we want all the numbers to be as close as possible to <math>\tfrac{17}4</math>, or <math>4.5</math>. Thus, we get the numbers <math>2</math>, <math>4</math>, <math>5</math>, and <math>6</math>. These multiply up to <math>2\cdot4\cdot5\cdot6 = \boxed{240}</math>. | ||
| − | + | ~pineconee | |
== See Also == | == See Also == | ||
| − | {{ | + | {{UNCO Math Contest box|n=II|year=2013|num-b=4|num-a=6}} |
[[Category:Intermediate Algebra Problems]] | [[Category:Intermediate Algebra Problems]] | ||
Latest revision as of 14:04, 30 April 2022
Problem
If the sum of distinct positive integers is 
, find the largest possible value of their product. Give both a set of
positive integers and their product. Remember to consider only sums of distinct numbers, and not 
or
, etc., which have repeated terms. You need not justify your answer on this question.
Solution
Intuitively, we want all the numbers to be as close as possible to 
, or 
. Thus, we get the numbers 
, 
, 
, and 
. These multiply up to 
.
~pineconee
See Also
| 2013 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNCO Math Contest Problems and Solutions | ||
