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We3D26522yso how would you know when you receive the right answer if it was bruteforced or not ... you r posting here after all

Chuck doesn't spy. He tampers with the communication and makes the senders believe that was the message they wanted to send.

Can you solve this without knowing msg5 up front? I have been attempting all morning lol

@notroot yeah I think your right  without msg5, I have been able to solve for Ay, By, and all the messages except for msg5 and msg0/6. I tried for the longest time to solve for even the w and x variables too but no luck. I wonder if you could somehow solve through graphing potential solution values.
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Riddle:
Alice and bob want to communicate a secret message, lets say it is an integer.
We will call this msg0.
You are Chuck, an interloper trying to spy on them and decode the message.
For keys, alice chooses a random integer w, another for x, and another for y. she also calculates a fourth variable, x+y = z
Bob follows the same procedure.
Suppose the numbers are too large to bruteforce.
Their exchange looks like this.
At step 1, alice calculates the following:
msg1 = alice.z+alice.w+msg0
she sends this message over the internet to bob.
the value of msg1 is 20838
then for our second step of the process, bob calculates msg2 = bob.z+bob.w+msg1
msg2 equals 32521
he then sends msg2 to alice, and again, you intercept and observe.
at step three, alice recieves bob's message, and calculates the following: msg3 = msg2(alice.x+alice.w+msg0)
msg3 equals 19249. Alice sends this to bob.
bob calculates msg4 = msg3(bob.x+bob.w)
msg4 equals 11000.
he sends msg4 to alice
at this stage, alice calculates ms5.
msg5 = (msg4(alice.y)+msg0.
alice sends this to bob.
bob recieves this final message and calculates
the sixth and final message, which is the original hidden msg0 alice wanted to send:
msg6 = msg5bob.y
What is the secret message?
I'll give anyone who solves it without bruteforcing, a free cookie.
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math