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@codekansas
Created April 30, 2020 01:41
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#!/usr/bin/env python3
"""Problem statement:
There is a teacher and 2 students in a classroom. The students are A and B.
The teacher thinks of 2 positive integers and tells the sum of those numbers
to student A without student B hearing it. Then tells their product to student
B without student A hearing it. After this, the teacher asks the 2 students
what was the 2 numbers.
First student A says: I don't know.
Then student B says: I don't know either.
After hearing this, student A says: Now I know.
Then student B says: Now I know them too.
What were the 2 numbers?
"""
def memoize(f):
memo = {}
def helper(x):
if x not in memo:
memo[x] = f(x)
return memo[x]
return helper
def _tup(x, y):
return (x, y) if x < y else (y, x)
@memoize
def add_decomp(s):
return {_tup(i, s - i) for i in range(1, s)}
@memoize
def prod_decomp(p):
return {_tup(i, p // i) for i in range(1, p) if p % i == 0}
@memoize
def a_first(s):
return len(add_decomp(s)) > 1
@memoize
def b_first(p):
return sum([a_first(i + j) for i, j in prod_decomp(p)]) > 1
@memoize
def a_second(s):
return sum([b_first(i * j) for i, j in add_decomp(s)]) == 1
@memoize
def b_second(p):
return sum([a_second(i + j) for i, j in prod_decomp(p)]) == 1
log = False
maxv = 10
for a in range(1, maxv):
for b in range(1, a + 1):
s, p = a + b, a * b
if log:
print(f'a: {a}, b: {b}, s: {s}, p: {p}', end=' :: ')
if not a_first(p):
if log:
print('a knows the first time')
continue
if not b_first(s):
if log:
print('b knows the first time')
continue
if not a_second(p):
if log:
print('a does not know the second time')
continue
if not b_second(s):
if log:
print('b does not know the second time')
continue
print(f'a: {a}, b: {b} works!')
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