MathDB

5

Part of 2014 ASDAN Math Tournament

Problems(5)

2014 Advanced #5

Source:

7/1/2022
Compute the smallest 99-digit number containing all the digits 11 to 99 that is divisible by 9999.
2014Advanced Topics Test
2014 Algebra #5

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7/8/2022
A positive integer kk is 20142014-ambiguous if the quadratics x2+kx+2014x^2+kx+2014 and x2+kx−2014x^2+kx-2014 both have two integer roots. Compute the number of integers which are 20142014-ambiguous.
2014Algebra Test
2014 General #5

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7/4/2022
Screws are sold in packs of 1010 and 1212. Harry and Sam independently go to the hardware store, and by coincidence each of them buys exactly kk screws. However, the number of packs of screws Harry buys is different than the number of packs Sam buys. What is the smallest possible value of kk?
2014General Test
2014 Team #5

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7/1/2022
Given a triangle ABCABC with integer side lengths, where BDBD is an angle bisector of ∠ABC\angle ABC, AD=4AD=4, DC=6DC=6, and DD is on ACAC, compute the minimum possible perimeter of △ABC\triangle ABC.
2014team test
2014 Geometry #5

Source:

7/12/2022
Consider a triangle ABCABC with AB=4AB=4, BC=3BC=3, and AC=2AC=2. Let DD be the midpoint of line BCBC. Find the length of ADAD.
2014Geometry Test