Math & Logic (Easy)Sharpen your logical thinking with these fundamental mathematical problems.

Check Prime Number

Problem Statement

Check if a given number is prime (only divisible by 1 and itself).

Solution

def is_prime(n):
    if n <= 1: return False
    for i in range(2, int(n**0.5) + 1):
        if n % i == 0:
            return False
    return True

Generate First N Primes

Problem Statement

Generate a list containing the first n prime numbers.

Solution

def generate_n_primes(n):
    primes = []
    num = 2
    while len(primes) < n:
        is_p = True
        for i in range(2, int(num**0.5) + 1):
            if num % i == 0:
                is_p = False
                break
        if is_p:
            primes.append(num)
        num += 1
    return primes

Find Factorial

Problem Statement

Calculate the factorial of a non-negative integer n (n!).

Solution

def factorial(n):
    res = 1
    for i in range(1, n + 1):
        res *= i
    return res

Check Armstrong Number

Problem Statement

Check if a number is an Armstrong number (sum of its digits each raised to the power of the number of digits equals the number itself).

Solution

def is_armstrong(n):
    s_num = str(n)
    k = len(s_num)
    res = sum(int(digit)**k for digit in s_num)
    return res == n

Reverse a Number

Problem Statement

Reverse the digits of an integer.

Solution

def reverse_number(n):
    rev = 0
    while n > 0:
        rev = rev * 10 + n % 10
        n //= 10
    return rev

Check Palindrome Number

Problem Statement

Determine if an integer is a palindrome (reads the same forward and backward).

Solution

def is_palindrome_num(n):
    return str(n) == str(n)[::-1]

Count Digits

Problem Statement

Count the total number of digits in an integer.

Solution

def count_digits(n):
    return len(str(abs(n)))

Sum of Digits

Problem Statement

Calculate the sum of the digits of a number.

Solution

def sum_digits(n):
    s = 0
    for d in str(abs(n)):
        s += int(d)
    return s

Find GCD

Problem Statement

Find the Greatest Common Divisor (GCD) of two numbers.

Solution

def find_gcd(a, b):
    while b:
        a, b = b, a % b
    return a

Find LCM

Problem Statement

Calculate the Least Common Multiple (LCM) of two numbers.

Solution

def find_lcm(a, b):
    def gcd(x, y):
        while y: x, y = y, x % y
        return x
    return abs(a * b) // gcd(a, b) if a and b else 0

Fibonacci Series

Problem Statement

Generate a list of the first n Fibonacci numbers.

Solution

def fibonacci(n):
    if n <= 0: return []
    if n == 1: return [0]
    fib = [0, 1]
    while len(fib) < n:
        fib.append(fib[-1] + fib[-2])
    return fib

Check Perfect Number

Problem Statement

Determine if a number is a perfect number (sum of its proper divisors equals the number itself).

Solution

def is_perfect(n):
    if n <= 1: return False
    s = 0
    for i in range(1, n // 2 + 1):
        if n % i == 0:
            s += i
    return s == n

Power of Number

Problem Statement

Calculate x raised to the power of y (x^y).

Solution

def power(x, y):
    return x ** y

Count Trailing Zeros

Problem Statement

Count the number of trailing zeros in n! (factorial).

Solution

def trailing_zeros(n):
    count = 0
    while n >= 5:
        n //= 5
        count += n
    return count

Check Leap Year

Problem Statement

Determine if a year is a leap year.

Solution

def is_leap_year(year):
    return (year % 4 == 0 and year % 100 != 0) or (year % 400 == 0)

Convert Decimal to Binary

Problem Statement

Convert a decimal number to its binary representation (string).

Solution

def dec_to_bin(n):
    return bin(n)[2:] if n >= 0 else "-" + bin(abs(n))[2:]

Convert Binary to Decimal

Problem Statement

Convert a binary string to its decimal integer equivalent.

Solution

def bin_to_dec(b_str):
    return int(b_str, 2)

Swap Two Numbers

Problem Statement

Swap the values of two variables.

Solution

def swap(a, b):
    return b, a

Find Largest of Three

Problem Statement

Return the maximum of three numbers.

Solution

def find_max_of_three(a, b, c):
    return max(a, b, c)

Check Even or Odd

Problem Statement

Determine if a number is even or odd.

Solution

def even_or_odd(n):
    return "Even" if n % 2 == 0 else "Odd"

Print Multiplication Table

Problem Statement

Return the first 10 multiples of a number as a list.

Solution

def multi_table(n):
    return [n * i for i in range(1, 11)]

Find Square Root

Problem Statement

Calculate the square root of a number (without built-in math.sqrt for practice).

Solution

def square_root(n):
    return n ** 0.5

Check Power of Two

Problem Statement

Determine if an integer is a power of two.

Solution

def is_power_of_two(n):
    return n > 0 and (n & (n - 1)) == 0

Count Set Bits

Problem Statement

Count the number of 1s in the binary representation of an integer (Hamming weight).

Solution

def count_set_bits(n):
    count = 0
    while n:
        n &= (n - 1)
        count += 1
    return count

Sum of Natural Numbers

Problem Statement

Calculate the sum of the first n natural numbers.

Solution

def sum_natural(n):
    return n * (n + 1) // 2

Find Cube of Number

Problem Statement

Calculate the cube of a given number (n^3).

Solution

def cube(n):
    return n ** 3

Check Strong Number

Problem Statement

Determine if a number is a Strong number (sum of the factorials of its digits equals the original number).

Solution

def is_strong(n):
    def fact(x):
        res = 1
        for i in range(1, x + 1): res *= i
        return res
    return sum(fact(int(d)) for d in str(n)) == n

Print Star Patterns (Basic)

Problem Statement

Return a string representing a 3x3 square of stars.

Solution

def star_square():
    return "\\n".join(["***"] * 3)

Find Highest Common Factor (HCF)

Problem Statement

Calculate the Highest Common Factor (HCF), which is another name for GCD.

Solution

def find_hcf(a, b):
    while b:
        a, b = b, a % b
    return a

Check Number Sign

Problem Statement

Determine if a number is positive, negative, or zero.

Solution

def check_sign(n):
    if n > 0: return "Positive"
    if n < 0: return "Negative"
    return "Zero"

Calculate Simple Interest

Problem Statement

Calculate simple interest using the formula: (P * R * T) / 100.

Solution

def simple_interest(p, r, t):
    return (p * r * t) / 100

Calculate Compound Interest

Problem Statement

Calculate compound interest (CI = P(1 + r/n)^(nt) - P).

Solution

def compound_interest(p, r, t):
    amount = p * (pow((1 + r / 100), t))
    return amount - p

Count Factors

Problem Statement

Count the total number of divisors (factors) of a given number.

Solution

def count_factors(n):
    return sum(1 for i in range(1, n + 1) if n % i == 0)

Find Average

Problem Statement

Calculate the average of a list of numbers.

Solution

def find_average(arr):
    return sum(arr) / len(arr) if arr else 0

Check Divisibility

Problem Statement

Check if number 'a' is divisible by number 'b'.

Solution

def is_divisible(a, b):
    return a % b == 0 if b != 0 else False

Generate Random Number (Basic)

Problem Statement

Simulate getting a random number by using a pseudo-random multiplier logic.

Solution

def pseudo_random(seed):
    # Linear Congruential Generator
    return (seed * 1103515245 + 12345) % (2**31)

Convert Celsius to Fahrenheit

Problem Statement

Formula: F = (C * 9/5) + 32.

Solution

def c_to_f(c):
    return (c * 9/5) + 32

Convert Fahrenheit to Celsius

Problem Statement

Formula: C = (F - 32) * 5/9.

Solution

def f_to_c(f):
    return (f - 32) * 5/9

Check Buzz Number

Problem Statement

A number is a Buzz number if it ends with 7 or is divisible by 7.

Solution

def is_buzz(n):
    return n % 10 == 7 or n % 7 == 0

Check Neon Number

Problem Statement

A number whose sum of digits of its square is equal to the number itself (e.g., 9: 9^2=81, 8+1=9).

Solution

def is_neon(n):
    sq = n * n
    s_digits = sum(int(d) for d in str(sq))
    return s_digits == n

Check Spy Number

Problem Statement

A number where the sum of its digits equals the product of its digits (e.g., 123: 1+2+3 = 6, 1*2*3 = 6).

Solution

def is_spy(n):
    digits = [int(d) for d in str(n)]
    s = sum(digits)
    p = 1
    for d in digits: p *= d
    return s == p

Find Smallest Digit

Problem Statement

Find the smallest numeric digit in a given integer.

Solution

def smallest_digit(n):
    return min(int(d) for d in str(abs(n)))

Find Largest Digit

Problem Statement

Find the largest numeric digit in a given integer.

Solution

def largest_digit(n):
    return max(int(d) for d in str(abs(n)))

Count Odd Digits

Problem Statement

Count how many odd numeric digits are in an integer.

Solution

def count_odd_digits(n):
    return sum(1 for d in str(abs(n)) if int(d) % 2 != 0)

Count Even Digits

Problem Statement

Count how many even numeric digits (including 0) are in an integer.

Solution

def count_even_digits(n):
    return sum(1 for d in str(abs(n)) if int(d) % 2 == 0)

Print Star Pattern (Triangle)

Problem Statement

Return a string representing a right-angled star triangle of height 3.

Solution

def star_triangle():
    return "\\n".join(["*" * i for i in range(1, 4)])

Print Number Pattern

Problem Statement

Return a string representing a number triangle (1, 12, 123) of height 3.

Solution

def num_triangle():
    return "\\n".join(["".join(map(str, range(1, i+1))) for i in range(1, 4)])

Check Harshad Number

Problem Statement

A Harshad (or Niven) number is an integer that is divisible by the sum of its digits.

Solution

def is_harshad(n):
    s_digits = sum(int(d) for d in str(n))
    return n % s_digits == 0 if s_digits != 0 else False

Sum of First N Numbers

Problem Statement

Calculate the sum of numbers from 1 up to n.

Solution

def sum_n(n):
    return n * (n + 1) // 2

Print Hollow Square Pattern

Problem Statement

Return a string for a 3x3 hollow square of stars.

Solution

def hollow_square():
    return "***\\n* *\\n***"

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Math & Logic (Easy) / Check Prime Number

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Check Prime Number

Check if a given number is prime (only divisible by 1 and itself).

1
Handle cases for n <= 1 (not prime).
2
Iterate from 2 up to the square root of n.
3
If n is divisible by any number in this range, it's not prime.
4
Otherwise, it is prime.

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