Solution to problem A in tonight's contest, with explanation of hashmaps

goodmorning.py

# A 'map' also known as a 'dictionary' also known as a 'hashmap':
# https://en.wikipedia.org/wiki/Hash_table
# It maps 'keys' to 'values'. Keys and values can be anything: strings, tuples, integers, floats...
# Here, the keys are integers and the values are lists of integers.
d = {
  1: [1,2,3,4,5,6,7,8,9,0],
  2: [2,3,5,6,8,9,0],
  3: [3,6,9],
  4: [4,5,6,7,8,9,0],
  5: [5,6,8,9,0],
  6: [6,9],
  7: [7,8,9,0],
  8: [8,9,0],
  9: [9],
  0: [0],
}

# The word 'path' comes from graph theory.
# https://en.wikipedia.org/wiki/Path_(graph_theory)
# A dictionary is essentially the adjacency list of a graph.
# You could say vertices in the graph are digits and an edge from V to W means your hand can go to W after you press V.
# A path is a list of vertices that are connected by edges.
# You can enumerate all the paths in a graph by brute force.

numbers = set()
for i in d:
    numbers.add(i)
    for j in d[i]:
        numbers.add(10*i+j)
        for k in d[j]:
            numbers.add(100*i+10*j+k)

# We get the closest number by finding the one in the set with the smallest absolute difference.
def findClosest(n):
    return min(numbers, key=lambda n: abs(num-n))