Can You Decipher The Secret Message?¶
Riddler Classic¶
This week’s Classic comes courtesy of Alexander Zhang of Lynbrook High School, California. Alexander won first place in the mathematics category at this year’s International Science and Engineering Fair for his work at the intersection of topology and medicine. He developed his own highly efficient algorithms to detect and remove defects (like “handles” or “tunnels”) from three-dimensional scans (e.g., MRI). Alexander has long had an interest in topology, which just might be related to his submitted puzzle.
Consider the following image showing a particular uppercase sans serif font:
Alphabet, upper case in sans serif font. Alexander thinks many of these letters are equivalent, but he leaves it to you to figure out how and why. He also has a message for you:
It may not look like much, but Alexander assures me that it is equivalent to exactly one word in the English language.
What is Alexander’s message?
Solution¶
Letters can be divided into the following loosely defined topographical groups:
- A Single Path:
C, G, I, J, L, M, N, S, U, V, W, Z
- A Single Path with a Branch:
E, F, T, Y
- A Single Path with two Branches:
H, K, X
- A Single Loop:
D, O
- A Single Loop with a Branch:
P, Q
- A Single Loop with two Branches:
A, R
- Two Loops:
B
Looking at the letters of YIRTHA:
- Y is from Group 2 with 4 possibilities.
- I is from Group 1 with 12 possibilities.
- R is from Group 6 with 2 possibilities.
- T is from Group 2 with 4 possibilities.
- H is from Group 3 with 3 possibilities.
- A is from Group 6 with 2 possibilities.
$4 \cdot 12 \cdot 2 \cdot 4 \cdot 3 \cdot 2 = 2,304$ unique 'words' that are equivalent to YIRTHA.
The R and A from the 3rd and 6th positions, along with the H from the 5th position, had me thinking. If the last letter is an R, none of H, K, or X in the 5th position seem to make a sensible word.
There were too many possibilities to list and check, although someone in the Riddler bunch probably did! I decided to use a bit of code.