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Bridge Building

by Bryan Lee, Nishant Pappireddi, and Olga Vinogradova


This is a giant Hashiwokakero logic puzzle. While it is possible to get close to the correct solution by using standard Hashi rules, it is probably quite daunting to do so without some extra constraint.

The key realization is that the "bridges" of the Hashi puzzle are also chemical bonds. This is lightly hinted at by charges on some of the circles and the fact that circled numbers do not go beyond four, the maximum number of bonds a carbon atom can have. In fact the backbone in the flavortext, in addition to being the courage needed for puzzle solving, also stands for a polymer backbone. Specifically, we have a polypeptide backbone connecting amino acids. Without this constraint there are multiple solutions to the logic puzzle.

Each node is a carbon, nitrogen, or oxygen atom. Bonds with hydrogen atoms are ignored. Identifying the backbone in the grid, which with one exception has a predictable unit pattern of -(2-3-4)- standing for -(N-C-C)-, helps greatly in constraining the logical solution path.

The solution figure shows the polypeptide backbone in black and amino acid functional groups in green. The (O) represents an oxygen atom and is used to disambiguate threonine. Single letter amino acid codes spell the final answer PROTEIN POWDER along the chain, read top left to bottom right.

Hashi puzzle solution with backbone bolded is shown here. Amino acid letters codes are marked at the functional group branching carbon.

Solution to the Hashiwokakero

The structure of the final polypeptide chain with amino acids identified (color shading for distinguishing boundaries between amino acids along the -(N-C-C)- polypeptide chain) is shown below:

A short peptide chain, with each amino acid on a different colored background. Above the chain are the letters PROTEINPOWDER.

The identity of amino acids in the answer is given by:

Letter CodeAmino Acid
EGlutamic Acid
DAspartic Acid
EGlutamic Acid

Author Notes:

This idea was pitched early on as the “obligatory chemistry puzzle.” While this puzzle is fairly light on chemistry compared to some gems found in past puzzle hunts, Hashi bridges were just asking to be made into a polypeptide chain as is and this puzzle wrote itself over half a day.