FiveThirtyEight's The Riddler

What is the Riddler?

The riddler is a weekly math, logic and probability problem hosted by, a statistically oriented politics, sports and culture blog.

If the answer is particularly cool or my solution can be extended, made interactable or generalized then I'll usually write it up. I've also created and submitted some problems that have been featured.

Submitted Problems

Barron Squares

This is a mathmatical object I made based off a problem on the /r/puzzles subreddit.

It is a square matrix such that each row's leftmost element times its rightmost element will equal the two inner numbers (in the example below, the top row has 6*7 = 42). Similarly, each column's uppermost element times the column's lowermost element equals the middle digits (in the example, the right column is 7*8 = 56), as read top to bottom.

6 4 2 7
4 2 0 5
8 4 8 6
8 6 4 8
4 x 4 Barron Square

This was then expanded on to be a 8x8 with two digit rows/columns being multiplied to get four digit products

6 2 4 5 8 8 7 4
6 1 2 9 2 8 4 8
1 1 0 4 6 2 4 2
7 6 4 4 8 4 5 9
8 3 6 8 0 6 8 2
2 8 2 4 6 4 8 8
2 7 1 7 8 2 6 6
7 8 1 6 3 8 2 1
8 x 8 Barron Square

We ended up finding all 1444 4x4 Barrons Squares, several hundred 8x8 and even a few 16x16 Barron Squares. This was featured as a Riddler Express for FiveThirtyEight.

A Geometric Puzzle

This is a problem about finding geometric subshapes and summing their areas. The problem was sent to me by a friend looking for help on homework

Find the area of the orange section

Problem Solutions

Putting Sharp Objects into Round Ones

This problem was about creating triangles in a unit circle and determining if the circle's center was enclosed. This was then expanded to a tetrahedron in a unit sphere. Visualizing each randomly generated shape helps verify the logic that determines if the center is enclosed is working correctly.

Results from 2d simulation

The probability that the shapes would enclose the center resulted in surprisingly nice 25% and 12.5%

Results from 3d simulation


This problem was about taking a state map, show below, and gerrymandering it until the maximum number of blue and red sections won.

Initial map with no districts drawn

We used a randomized search that would try to slightly move districts, check continuity and then check the voting results. The method resulted in uniquely shaped maps that optimized each side's winningness.

Districts move their boundaries each iteration

Map with districts drawn optimized for blue. Blue wins 5/7 districts after 100,000 iterations

National Squishyball League Championship

This problem was about taking a competition where you could choose the number of games at the cost of prize money. It was your job to find the number of games that yielded the maximum expected return.

Expected value for each number of games

This was multiplied by the chance the Axegrinders won the series to yield the expected value of the tournament.

Axegrinder's Expected Value for the tournament


Matching Game

A Classic Construction Problem

An Amphibious Enigma

Bright Lights, Big City

The Purge

A Painting Puzzle

Pick a Card, Any Card

A Puzzle About Domestic Boundaries

An Impromptu Gambling Problem

Can You Survive This Deadly Board Game?

Count Von Count


Space Race

Which Geyser Gushes First?

What’s The Best Way To Drop A Smartphone?