Program to find all the solutions to the "The Fours Have It" math worksheet

the fours have it.py

## Well, almost all of them. There are solutions for 13 but this doesn't find those for some odd reason
import sys


def sqrt(x):
    try:
        return {169: 13, 144: 12, 121: 11, 100: 10, 81: 9,
                64: 8, 49: 7, 36: 6, 25: 5, 16: 4, 9: 3, 4: 2}[x]
    except KeyError:
        raise ValueError("don't want floats") from None


def fact(n):
    assert 2 < n < 10
    prod = 1
    for i in range(1, n+1):
        prod *= i
    return prod


def mpow(x, y):
    if int(x) != x:
        raise ValueError
    if x > 9999 or y > 99999:
        raise OverflowError
    return pow(x, y)


operators = [
    # format str, is 1-op, noncommutative
    ("{}+{}", False, False),  # a+b
    ("{}-{}", False, True),  # a-b
    ("{}*{}", False, False),  # a*b
    ("{}/{}", False, True),  # a/b
    ("mpow({}, {})", False, True),  # a**b
    ("sqrt({})", True, None),  # sqrt(a)
    ("fact({})", True, None),  # a!
    ("{}{}", False, True),  # two 4s -> 44
]


def expressions(num=4, count=4, cando1op=2):
    if count == 0:
        raise RuntimeError
    out = []
    for op in operators:
        if op[1]:
            if cando1op:
                parts = expressions(num, count, cando1op-1)
                # it's a one-expression operator, there's nothing else we can do
                for p in parts:
                    out.append(op[0].format(p))
        elif count > 1:
            parts = expressions(num, count-1)
            for p in parts:
                out.append(op[0].format(p, num))
                if op[2]:
                    out.append(op[0].format(num, p))
    return out or [str(num)]


print("Generating expressions...")
ex = expressions(4, 4)

d = {}

num = len(ex)
i = 0
th = 0
print(num)
# evaluate all the expressions
for e in ex:
    try:
        v = eval(e)
        if v not in d:
            d[v] = set()
        d[v].add(e)
    except KeyboardInterrupt:
        raise
    except:
        pass
    i += 1
    if i == 1000:
        # print progress report
        th += 1
        print(f"{th}000/{num}")
        i = 0

try:
    if "idlelib" in sys.modules:
        raise ModuleNotFoundError  # running under IDLE breaks IPython REPL
    import IPython
    IPython.embed()
except ModuleNotFoundError:
    import code
    code.InteractiveConsole(locals=globals()).interact()