MathDB

3

Part of 2000 Harvard-MIT Mathematics Tournament

Problems(7)

2000 Advanced Topics #3: Infinite Summation

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6/21/2012
Evaluate ∑n=1∞1n2+2n\displaystyle\sum_{n=1}^\infty \dfrac{1}{n^2+2n}.
2000 Guts #3: Coloring a cube

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10/12/2014
Using 33 colors, red, blue and yellow, how many different ways can you color a cube (modulo rigid rotations)?
geometry3D geometrygeometric transformationrotation
2000 Algebra #3: Difference between Mean and Median

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10/5/2014
Five students take a test on which any integer score from 00 to 100100 inclusive is possible. What is the largest possible difference between the median and the mean of the scores?
2000 HMMT RMT Geometry # 3

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3/3/2024
Find PBPB, given that PA=15PA = 15, PC=20PC = 20, PD=7PD = 7, and ABCDABCD is a square. https://cdn.artofproblemsolving.com/attachments/7/a/cc5bf99986fea1cd75e57fe1117a4d04d3eae3.png
geometry
2000 Oral #3: Inequality

Source:

10/6/2014
Suppose the positive integers a,b,ca,b,c satisfy an+bn=cna^n+b^n=c^n, where nn is a positive integer greater than 11. Prove that a,b,c>na,b,c>n. (Note: Fermat's Last Theorem may not be used)
inequalities
2000 HMMT RMT Team #3

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3/8/2024
Find the sum of all integers from 11 to 10001000 inclusive which contain at least one 77 in their digits, i.e. find 7+17+...+979+987+997.7 + 17 +... + 979 + 987 + 997.
algebra
2000 HMMT RMT General #3

Source:

3/8/2024
A twelve foot tree casts a five foot shadow. How long is Henry’s shadow (at the same time of day) if he is five and a half feet tall?
algebrageometry