plates.py

#!/usr/bin/python3

# https://www.reddit.com/r/FellowKids/comments/drbnxj/mathematics_meets_rfellowkids/

def is_pal(ds):
    return ds[0] == ds[2]

def group(n):
    for d1 in range(n):
        for d2 in range(n):
            for d3 in range(n):
                yield [d1, d2, d3]

n = 0
for g1 in group(3):
    for g2 in group(5):
        if is_pal(g1) or is_pal(g2):
            n += 1

print(n)