We have a 8 figure number, lets call it $N_1=a_1a_2a_3a_4a_5a_6a_7a_8$. Prove that if we interchange two numbers (for example $N_2=a_1a_2a_4a_3a_5a_6a_7a_8$ and $N_1 \neq N_2$) then the rest we get by dividing $N_1$ and $N_2$ with 23 isn't the same. Then prove that if we change one number (for example: $N_3=a_1a_2ba_4a_5a_6a_7a_8$ and $b\neq a_3$) the rest we get by dividing $N_1$ and $N_3$ by 23 is not the same.
Then prove that this is not true if we divide the numbers by 24. I mean, that we can find $N_1, N_2$ and $N_3$ defined as I said before that after dividing by 24 the rest is the same.
I do not even know how to start. Thanks in advance.