After the 18.701 midterm (9:30 AM to 11 AM Eastern) on 10/27/2026, I will give each of the seven problems on the test a "difficulty rating", from 0% to 100%. When I am allowed to discuss the test, I will resolve the market to the highest rating of the seven. Please do not bet on this market when testing is happening (9:30 AM to 11 AM).

Here are some examples of my ratings for past 18.701 problems. Generally, if a problem takes me more than 10-15 minutes of thinking (not including writeup and working out small annoying details), I will probably consider it fairly nontrivial for the purposes of this market. However, for the sake of this judgment, I generally will not consider busywork in a problem to add significantly to its difficulty.

• 5%: The past quiz problem about orthogonal projections and det(A-2I)

• 5%: The past quiz problem about homomorphisms S3 -> C3

• 5%: The past pset problem about <1, sqrt2> in R

• 10%: The past pset problem about sum (-1)^i dim V_i = 0 in an exact sequence of vector spaces

• 25%: The review party problem about automorphisms of C9 x C9

• 30%: The review party problem about the Jordan Normal Form of the matrix expressed as blocks J_n, I_n J_n \\ 0, J_n

• 35%: Problem 2 on my practice quiz

• 40%: The past pset problem about whether O_n is isomorphic to SO_n x C2

• 40%: The classification of groups of order pq (assuming we are allowed to cite the relevant difficult lemmas without proof)

• 60%: Problem 1 on my practice quiz

• 80%: The proof that if a finite group G has an automorphism that is also an involution which only fixes the identity, then G is abelian

• 85%: The proof that if p is the smallest prime dividing |G| for a finite group G, then a subgroup of index p is normal

• 95%: The proof that nilpotent matrices can be expressed in Jordan Normal Form

• 95%: The generalized eigenspace decomposition step in the proof of the existence of the Jordan Normal Form

Obviously, I will not bet on this market.