Intersecting Powers and Roots

Here is an interesting little question. Its answer is simple, and not hard to see just by graphing examples; yet the algebra is easy to get wrong, as we’ll see several times. And subtle errors deserve study.

Parallel Vectors: Missing a Solution

(A new question of the week) We were recently asked to check work on an interesting little question about parallel vectors, and I was almost convinced that there was no solution … until I realized there was one! How was it missed? How can we avoid doing that? That’s our goal today.

Probability: Cards vs Dice

(A new question of the week) A couple recent questions involved related subtleties in probability and combinatorics. Both were about apparent conflicts between similar problems involving cards and dice.

Non-homogeneous Recurrence Relations

(A new question of the week) A recent question asked us to find errors in solving recurrence relations by the method of undetermined coefficients. We’ll see several things that can go wrong, and correct some misunderstandings.