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• 03:16, 21 October 2014 (diff | hist) . . (+798)‎ . . N 2006 UNCO Math Contest II Problems/Problem 11 ‎ (Created page with "== Problem == Call the figure below a "<math>4</math>-tableau" shape. Determine the number of rectangles of all sizes contained within this shape. Note that a square is conside...")
• 03:15, 21 October 2014 (diff | hist) . . (+283)‎ . . N 2006 UNCO Math Contest II Problems/Problem 10 ‎ (Created page with "== Problem == How many triples of positive integers <math>a,b</math> and <math>c</math> are there with <math>a<b<c</math> and <math>a+b+c=401</math>. ==Solution== ==See Also=...")
• 03:15, 21 October 2014 (diff | hist) . . (+440)‎ . . N 2006 UNCO Math Contest II Problems/Problem 9 ‎ (Created page with "== Problem == Determine three positive integers <math>a,b</math> and <math>c</math> that simultaneously satisfy the following three conditions: (i) <math>a<b<c</math> (ii) Ea...")
• 03:13, 21 October 2014 (diff | hist) . . (+361)‎ . . N 2006 UNCO Math Contest II Problems/Problem 8 ‎ (Created page with "== Problem == Find all positive integers <math>n</math> such that <math>n^3-12n^2+40n-29</math> is a prime number. For each of your values of <math>n</math> compute this cubic ...")
• 03:13, 21 October 2014 (diff | hist) . . (+493)‎ . . N 2006 UNCO Math Contest II Problems/Problem 7 ‎ (Created page with "== Problem == The five digits <math>a,b,c,d</math> and <math>e</math> of <math>55225</math> are such that <math>a=b=e</math> and <math>c=d</math>; in addition, <math>55225=235^2...")
• 03:12, 21 October 2014 (diff | hist) . . (+446)‎ . . N 2006 UNCO Math Contest II Problems/Problem 6 ‎ (Created page with "== Problem == The sum of all of the positive integer divisors of <math>6^2=36</math> is <math>1+2+3+4+6+9+12+18+36=91</math> (a) Determine a nice closed formula (i.e. without ...")
• 03:12, 21 October 2014 (diff | hist) . . (+641)‎ . . N 2006 UNCO Math Contest II Problems/Problem 5 ‎ (Created page with "== Problem == In the figure <math>BD</math> is parallel to <math>AE</math> and also <math>BF</math> is parallel to <math>DE</math>. The area of the larger triangle <math>ACE</m...")
• 03:11, 21 October 2014 (diff | hist) . . (+287)‎ . . N 2006 UNCO Math Contest II Problems/Problem 4 ‎ (Created page with "== Problem == Determine all positive integers <math>n</math> such that <math>n^2+3</math> divides evenly (without remainder) into <math>n^4-3n^2+10</math> ? ==Solution== ==Se...")
• 03:10, 21 October 2014 (diff | hist) . . (+657)‎ . . N 2006 UNCO Math Contest II Problems/Problem 1 ‎ (Created page with "== Problem == If a dart is thrown at the <math>6\times 6</math> target, what is the probability that it will hit the shaded area? <asy> filldraw((2,2)--(4,6)--(6,6)--(6,4)--cyc...")
• 03:09, 21 October 2014 (diff | hist) . . (+409)‎ . . N 2006 UNCO Math Contest II Problems/Problem 2 ‎ (Created page with "== Problem == If <math>a,b</math> and <math>c</math> are positive integers, how many integers are strictly between the product <math>abc</math> and <math>(a+1)(b+1)(c+1)</math> ...")
• 03:07, 21 October 2014 (diff | hist) . . (-1)‎ . . m 2006 UNCO Math Contest II Problems/Problem 3 ‎ (→‎See Also)
• 03:07, 21 October 2014 (diff | hist) . . (+102)‎ . . 2006 UNCO Math Contest II Problems/Problem 3 ‎ (→‎See Also)
• 03:05, 21 October 2014 (diff | hist) . . (+367)‎ . . N 2006 UNCO Math Contest II Problems/Problem 3 ‎ (Created page with "== Problem == The first 14 integers are written in order around a circle. Starting with 1, every fifth integer is underlined. (That is <math>1,6,11,2,7,\ldots</math>). What is ...")
• 22:14, 20 October 2014 (diff | hist) . . (+774)‎ . . m 2006 UNCO Math Contest II Problems ‎
• 22:00, 20 October 2014 (diff | hist) . . (+1,660)‎ . . m 2006 UNCO Math Contest II Problems ‎
• 21:40, 20 October 2014 (diff | hist) . . (+2,177)‎ . . N 2006 UNCO Math Contest II Problems ‎ (Created page with "UNIVERSITY OF NORTHERN COLORADO MATHEMATICS CONTEST FINAL ROUND January 28,2006. For Colorado Students Grades 7-12. ==Problem 1== If a dart is thrown at the <math>6\times 6</...")
• 21:07, 20 October 2014 (diff | hist) . . (+1,118)‎ . . N 2006 UNCO Math Contest II ‎ (Created page with "'''2006 UNCO Math Contest''' problems and solutions. The test was held on January 28, 2006. The first link contains the full se...") (current)
• 21:06, 20 October 2014 (diff | hist) . . (+64)‎ . . m University of Northern Colorado Math Contest ‎ (→‎Past Exams)
• 15:40, 20 October 2014 (diff | hist) . . (0)‎ . . m 1993 UNCO Math Contest II Problems ‎ (→‎Problem 6) (current)
• 15:39, 20 October 2014 (diff | hist) . . (-2)‎ . . m 1993 UNCO Math Contest II Problems/Problem 6 ‎ (→‎Problem)
• 02:54, 20 October 2014 (diff | hist) . . (+748)‎ . . N 1993 UNCO Math Contest II Problems/Problem 10 ‎ (Created page with "== Problem == The scalene triangle <math>ABC</math> has side lengths <math>51, 52, 53.</math> <math>AD</math> is perpendicular to <math>BC.</math> <asy> draw((0,0)--(52,0)--(24,...")
• 02:53, 20 October 2014 (diff | hist) . . (+703)‎ . . N 1993 UNCO Math Contest II Problems/Problem 9 ‎ (Created page with "== Problem == Let <math>P</math> be a point inside the rectangle <math>ABCD</math>. If <math>AP=5</math> , <math>BP=11</math> and <math>CP=10</math>, find the length of <math>DP...")
• 02:53, 20 October 2014 (diff | hist) . . (+420)‎ . . N 1993 UNCO Math Contest II Problems/Problem 8 ‎ (Created page with "== Problem == For what integer value of <math>n</math> is the expression <cmath>\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\cdots +\frac...")
• 02:52, 20 October 2014 (diff | hist) . . (+553)‎ . . N 1993 UNCO Math Contest II Problems/Problem 7 ‎ (Created page with "== Problem == Choose four numbers by circling exactly one number in each horizontal row, and one number in each vertical column. Compute the product of these four numbers. Expla...")
• 02:52, 20 October 2014 (diff | hist) . . (+465)‎ . . N 1993 UNCO Math Contest II Problems/Problem 6 ‎ (Created page with "== Problem == Observe that <cmath>\begin{align*} 2^2+3^2+6^3 &= 7^2 \\ 3^2+4^2+12^3 &= 13^2 \\ 4^2+5^2+20^3 &= 21^2 \\ \end{align*}</cmath> (a) Find integers <math>x</math> a...")
• 02:51, 20 October 2014 (diff | hist) . . (+300)‎ . . N 1993 UNCO Math Contest II Problems/Problem 5 ‎ (Created page with "== Problem == A collection of <math>25</math> consecutive positive integers adds to <math>1000.</math> What are the smallest and largest integers in this collection? == Soluti...")
• 02:50, 20 October 2014 (diff | hist) . . (+641)‎ . . N 1993 UNCO Math Contest II Problems/Problem 4 ‎ (Created page with "== Problem == The table gives some of the straight line distances between certain pairs of cities. for example the distance between city <math>A</math> and city <math>B</math> i...")
• 02:50, 20 October 2014 (diff | hist) . . (+320)‎ . . N 1993 UNCO Math Contest II Problems/Problem 3 ‎ (Created page with "== Problem == A student thinks of four numbers. She adds them in pairs to get the six sums <math>9,18,21,23,26,35.</math> What are the four numbers? There are two different so...")
• 02:49, 20 October 2014 (diff | hist) . . (+312)‎ . . N 1993 UNCO Math Contest II Problems/Problem 2 ‎ (Created page with "== Problem == Determine the digit in the <math>623^{rd}</math> place after the decimal point in the repeating decimal for: <cmath>\frac{1}{9}+\frac{2}{99}+\frac{3}{999}.</cmath>...")
• 02:49, 20 October 2014 (diff | hist) . . (+601)‎ . . N 1993 UNCO Math Contest II Problems/Problem 1 ‎ (Created page with "== Problem == How many times must one shoot at this target, and which rings must one hit in order to score exactly <math>100</math> points. <asy> draw(circle((0,0),1),black); d...")
• 02:47, 20 October 2014 (diff | hist) . . (0)‎ . . m 1993 UNCO Math Contest II Problems ‎
• 02:44, 20 October 2014 (diff | hist) . . (+714)‎ . . 1993 UNCO Math Contest II Problems ‎
• 02:13, 20 October 2014 (diff | hist) . . (+1,116)‎ . . 1993 UNCO Math Contest II Problems ‎
• 01:59, 20 October 2014 (diff | hist) . . (+2,589)‎ . . N 1993 UNCO Math Contest II Problems ‎ (Created page with "UNIVERSITY OF NORTHERN COLORADO MATHEMATICS CONTEST FINAL ROUND February 13,1993. For Colorado Students Grades 7-12. ==Problem 1== How many times must one shoot at this target...")
• 01:40, 20 October 2014 (diff | hist) . . (+1,100)‎ . . N 1993 UNCO Math Contest II ‎ (Created page with "'''1993 UNCO Math Contest''' problems and solutions. The test was held on February 13, 1993. The first link contains the full s...") (current)
• 01:39, 20 October 2014 (diff | hist) . . (+32)‎ . . m University of Northern Colorado Math Contest ‎
• 01:23, 20 October 2014 (diff | hist) . . (+614)‎ . . N 2007 UNCO Math Contest II Problems/Problem 10 ‎ (Created page with "== Problem == A quaternary “number” is an arrangement of digits, each of which is <math>0, 1, 2, 3.</math> Some examples: <math>001, 3220, 022113.</math> (a) How many <math...")
• 01:21, 20 October 2014 (diff | hist) . . (+769)‎ . . N 2007 UNCO Math Contest II Problems/Problem 9 ‎ (Created page with "== Problem == A circle is inscribed in an equilateral triangle whose side length is <math>2</math>. Then another circle is inscribed externally tangent to the first circle but i...")
• 01:20, 20 October 2014 (diff | hist) . . (+756)‎ . . N 2007 UNCO Math Contest II Problems/Problem 8 ‎ (Created page with "== Problem == A regular decagon <math>P_1P_2P_3\cdots P_{10}</math> is drawn in the coordinate plane with <math>P_1</math> at <math>(2,0)</math> and <math>P_6</math> at <math>(8...")
• 01:20, 20 October 2014 (diff | hist) . . (+604)‎ . . N 2007 UNCO Math Contest II Problems/Problem 7 ‎ (Created page with "== Problem == (a) Express the infinite sum <math>S= 1+ \frac{1}{3}+\frac{1}{3^2}+ \frac{1}{3^3}+ \cdots</math> as a reduced fraction. (b) Express the infinite sum <math>T=\frac...")
• 01:19, 20 October 2014 (diff | hist) . . (+344)‎ . . N 2007 UNCO Math Contest II Problems/Problem 6 ‎ (Created page with "== Problem == (a) Demonstrate that every odd number <math>2n+1</math> can be expressed as a difference of two squares. (b) Demonstrate which even numbers can be expressed as a ...")
• 01:18, 20 October 2014 (diff | hist) . . (+2,297)‎ . . N 2007 UNCO Math Contest II Problems/Problem 5 ‎ (Created page with "== Problem == Ten different playing cards have the numbers <math>1, 1, 2, 2, 3, 3, 4, 4, 5, 5</math> written on them as shown. Three cards are selected at random without replac...")
• 01:17, 20 October 2014 (diff | hist) . . (+354)‎ . . N 2007 UNCO Math Contest II Problems/Problem 4 ‎ (Created page with "== Problem == If <math>x</math> is a primitive cube root of one (this means that <math>x^3 =1</math> but <math>x \ne 1</math>) compute the value of <cmath>x^{2006}+\frac{1}{x^{2...")
• 01:17, 20 October 2014 (diff | hist) . . (+521)‎ . . N 2007 UNCO Math Contest II Problems/Problem 3 ‎ (Created page with "== Problem == State the general rule illustrated here and prove it: <math> 1 ,\quad \begin{tabular}{cc} 1&1\\1&2\end{tabular} ,\quad \begin{tabular}{ccc} 1&1&1\\1&2&2\\1&2&3\e...")
• 01:16, 20 October 2014 (diff | hist) . . (+344)‎ . . N 2007 UNCO Math Contest II Problems/Problem 2 ‎ (Created page with "== Problem == In Grants Pass, Oregon <math>\frac{4}{5}</math> of the men are married to <math>\frac{3}{7}</math> of the women. What fraction of the adult population is married?...")
• 01:15, 20 October 2014 (diff | hist) . . (+295)‎ . . N 2007 UNCO Math Contest II Problems/Problem 1 ‎ (Created page with "== Problem == Express the following sum as a whole number: <math>1+ 2 - 3 + 4 + 5 - 6 + 7 + 8 - 9 +10 +11-12 +\cdots + 2005 + 2006 - 2007.</math> == Solution == == See Also ...")
• 01:14, 20 October 2014 (diff | hist) . . (+1,019)‎ . . 2007 UNCO Math Contest II Problems ‎ (→‎Problem 5)
• 00:49, 20 October 2014 (diff | hist) . . (+836)‎ . . 2007 UNCO Math Contest II Problems ‎ (→‎Problem 5)
• 00:06, 20 October 2014 (diff | hist) . . (+218)‎ . . 2007 UNCO Math Contest II Problems ‎ (→‎Problem 9)
• 23:53, 19 October 2014 (diff | hist) . . (+183)‎ . . m 2007 UNCO Math Contest II Problems ‎ (→‎Problem 8)

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