Programming

Hiya,
I was wondering if anyone had any recourses for learning to make cryptography programs in Python? I managed to make a caesar cipher a while back in 2021 or ’22, but gave up when I got to affine lol – I want to try again with more experience!

Thank you! I’ll look into Cracking Code with Python – I also found “A book on Classical Cryptography” by Madness last night, and that seems really helpful. If anyone in the future wants to read it, you can find it here, or you could find it on the BOSS training recourses.

I am guessing this is the first in a series of coding challenges, so have at it! I think the setter is as interested in the code you write as in the arithmetical answer! I will hold off on publishing your solutions for a while so others can have a go. Harry

Hopefully a reasonably easy one to kick off with.

******************************************************************** Question #1
Find a number X that when divided by 4 leaves a remainder of 3 and
when divided by 5 leaves a remainder of 1 and when divided by 7 leaves a
remainder of 2 and when divided by 11 also leaves a remainder of 2 and
when divided by 17 leaves a remainder of 12. (with X > 5,000 & x < 50,000)

—————– same question put another way
Find X
when X is divided by 4,5,7,11,17 and in turn leaves the remainders 3,1,2,2,12
(with X being greater than 5,000 but less than 50,000)

For all questions: Give your code and the printout from it.

As you wish Harry: I claim to have made a solution!

Cool problem Bytes! I’m looking forwards to your next ones. How many will there be?

Hey coders, where are you?
With 1,000’s of participants I thought there would be at least half a dozen
replies to Question #1.

If you are wandering. . .
It does not matter how your code is done (what it looks like) as long as it
produces the results needed, no one will say you could have done it in a better
way, so don’t shy away from posting.

When others post code we may all learn something from it.

================================================ QUESTION #2

Write code in your chosen language and give answers to the following?

Find a 4 digit positive integer N that has 60 divisors (includes 1 and N) and
is also the sum of 42 consecutive primes. N and list the 42 primes.

Show your code and its output giving the answer to the number and the primes.

The heading of this thread is Programming so it is not all about math solving.
On that basis here is

======================================================== Question #3
WAYS WITH MONEY

In how many ways can UK 1 pound (100 pence) be given as change using all the UK coins?
UK Coins are: 1p,2p,5p,10p,20P,50p,£1(100p) and £2(200p), we disregard the £2 coin here.

HERE ARE THE THE FIRST FIVE AND LAST FIVE SETS THAT MY CODE GAVE
I have edit replaced some values with a ? (else it would give the answer away)

\\ ===================== PROGRAM OUTPUT ======================
\\ set#) coin count of(coin value)
\\ 1) 0(1p) 0(2p) 0(5p) 0(10p) 0(20p) 0(50p) 1(100p)
\\ 2) 0(1p) 0(2p) 0(5p) 0(10p) 0(20p) 2(50p) 0(100p)
\\ 3) 0(1p) 0(2p) 0(5p) 3(10p) 4(20p) 1(50p) 0(100p)
\\ 4) 0(1p) 0(2p) 0(5p) 4(10p) 2(20p) 1(50p) 0(100p)
\\ 5) 0(1p) 0(2p) 0(5p) 5(10p) 0(20p) 1(50p) 0(100p)
\\ ?) 95(1p) 0(2p) 0(5p) 0(10p) 1(20p) 0(50p) 0(100p)
\\ ?) 95(1p) 0(2p) 1(5p) 0(10p) 0(20p) 0(50p) 0(100p)
\\ ?) 96(1p) 2(2p) 0(5p) 0(10p) 0(20p) 0(50p) 0(100p)
\\ ?) 98(1p) 1(2p) 0(5p) 0(10p) 0(20p) 0(50p) 0(100p)
\\ ?) 100(1p) 0(2p) 0(5p) 0(10p) 0(20p) 0(50p) 0(100p)

\\ The number of possible ways (sets) is: ?

================= TASK

Write Code (function) and have it display the first and last TEN sets similar to the above.

SHOW YOUR CODE AND ITS OUTPUT

Question 2:

Solution: 5040
Sum of 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229.

I just checked all the 4-digit sums of 42 consecutive primes.

import math

def generate_primes(n): # Sieve of Eratosthenes
  nums = [2] + [i for i in range(3, n + 1, 2)]
  _primes = set()
  
  for i in range(3, int(n**0.5)):
    for j in range(i**2, n + 1, i):
      _primes.add(j)
  
  return list(filter(lambda x: x not in _primes, nums))

def primeSlicer(): # Finds all sums of 42 consecutive primes
    primes = generate_primes(355) # Stops at the last 4-digit num
    for i in range(len(primes) - 41):
        yield sum(primes[i: i+42])
        
def divisorCounter(num):
    counter = 0
    for i in range(1, int(num**0.5) + 1):
        if (num % i == 0): # Sorts out square numbers here.
            counter += 1 if i == num // i else 2

    return counter
    
for v in primeSlicer(): # Checks each prime number for the number of divisors
    if divisorCounter(v) == 60:
        print(v)