MathDB

2

Part of 2014 ASDAN Math Tournament

Problems(8)

2014 Advanced #2

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7/1/2022
Compute the number of integers between 11 and 100100, inclusive, that have an odd number of factors. Note that 11 and 44 are the first two such numbers.
2014Advanced Topics Test
2014 Advanced Tiebreaker #2

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7/1/2022
Compute the number of positive integers less than or equal to 1000010000 which are relatively prime to 20142014.
2014Advanced Topics Tiebreaker
2014 Algebra #2

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7/8/2022
Let aa and bb be positive integers such that a>ba>b and the difference between a2+ba^2+b and a+b2a+b^2 is prime. Compute all possible pairs (a,b)(a,b).
2014Algebra Test
2014 Algebra Tiebreaker #2

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7/9/2022
Let aa and bb be the roots of the quadratic x2−7x+cx^2-7x+c. Given that a2+b2=17a^2+b^2=17, compute cc.
2014Algebra Tiebreaker
2014 General #2

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7/4/2022
Sally rolls an 88-sided die with faces numbered 11 through 88. Compute the probability that she gets a power of 22.
2014General Test
2014 Team #2

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7/1/2022
Consider all right triangles with integer side lengths that form an arithmetic sequence. Compute the 20142014th smallest perimeter of all such right triangles.
2014team test
2014 Geometry #2

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7/12/2022
Let ABCABC be a triangle with sides AB=19AB=19, BC=21BC=21, and AC=20AC=20. Let ω\omega be the incircle of ABCABC with center II. Extend BIBI so that it intersects ACAC at EE. If ω\omega is tangent to ACAC at the point DD, then compute the length of DEDE.
2014Geometry Test
2014 Geometry Tiebreaker #2

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7/1/2022
Let RICERICE be a quadrilateral with an inscribed circle OO such that every side of RICERICE is tangent to OO. Given taht RI=3RI=3, CE=8CE=8, and ER=7ER=7, compute ICIC.
2014Geometry Tiebreaker