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52Is there a rule that ALL letters must represent only 1-digit integer ?

P.S. I'm a bit offended that you included Raoul in the solvers list. A solution must be backed by a proof, that is the whole pupose. I'd be pleased and encouraged if you remove his name from the list if he fails to submit a proof within next 3 days.

280Pool ProUsing a similar approach to Satya, I get 64 for problem 5.

280Pool ProYes, after figuring out I=8 am M=4 always, I just listed out all the possible values for the rest. Each of these gives eight solutions:

O=0/7 N=7/0 H=2 K=5 G=1/3/6/9

O=0/7 N=7/0 H=3 K=6 G=1/2/5/9

O=0/7 N=7/0 H=6 K=9 G=1/2/3/5

O=1/6 N=6/1 H=0 K=3 G=2/5/7/9

O=1/6 N=6/1 H=2 K=5 G=0/3/7/9

O=2/5 N=5/2 H=0 K=3 G=1/6/7/9

O=2/5 N=5/2 H=3 K=6 G=0/1/7/9

O=2/5 N=5/2 H=6 K=9 G=0/1/3/7

6,864Pool Forum VIPYou're doing it wrong. I'm working on a solution, I'll get back to you when I finish... earliest after Christmas...

4,114modBesides logic and mathematics, Problem 5 does not necessarily involve extreme manipulation of multiple expressions (as in calculus and number theory). Solving cryptograms is simply about understanding the mechanism of the given mathematical puzzle.

Some hints for Problem 5:For instance, if I want to find the possible distinct candidates for the following...

Then, I can see that the possibilities are...

If you know that another variable is 7, the second set is eliminated as well as A = 7.

If you have done some number and/or math puzzles, like Kakuro, you should know that there exists unidentified candidates for each box. Inputting one value in a box eliminates at least a pair of candidates, containing that number. If no candidate exists in any pair possibility, there must be the mistake in the puzzle. This is different from cryptogram, but that is how puzzles are.

I have more problems to put up, but I am going to wait for the correct responses.

Good luck to you all!

280Pool ProOops, you are right... i had some cases with a leading 0. The answer should be 48:

O=0/7 N=7/0 H=2 K=5 G=1/3/6/9

O=0/7 N=7/0 H=3 K=6 G=1/2/5/9

O=0/7 N=7/0 H=6 K=9 G=1/2/3/5

O=1/6 N=6/1 H=2 K=5 G=0/3/7/9

O=2/5 N=5/2 H=3 K=6 G=0/1/7/9

O=2/5 N=5/2 H=6 K=9 G=0/1/3/7

2,239Pool Champion2,239Pool Championi also agree

6,864Pool Forum VIPI would start from the fact that since O, N and G don't change from HONG to KONG, then these additions must end in zero: 7+O+6+N, 5+M+1+I, I+0. The two latter ones added with the digits you carry from the column right to them. Am I correct? H can not be bigger than 7.

Leading digits can't be zero – does that mean the letters I, H and K?

4,114modThe answer is correct. I guess that I have to adjust the rules a bit since there aren't many members here. Anyway, I am going to post the solution for difficult problems that can't be easily solved by many members.

That is correct!

I did that already.

52Oh, now I know where I made a mistake... I listed all the possible solutions for O=0/1/2 and N=7/6/5, but I miscounted them as 25 instead of 24... So when I doubled, the answer was more by 2. Anyway, I'm content that atleast I got the logic right.

4,114modGreat to hear! Guess you earn a point for almost arriving to the correct answer, even though @_raoul found the correct one first!

4,114modLet's start with non-mathematical puzzle....

Problem 7 - Sudoku Time! (Hard)Time Limit:1 weekProblem 8 - Math in 8 Ball Pool: So Much Winning! (Easy)Time Limit:1 week6,864Pool Forum VIP2,239Pool Championu have to find how many ways u can reach that solution

4,114modFor Problem 8, each letter must be distinct. I revised the problem. In case you are not familiar with the term "permuted string", 12 and 21 are permuted strings. Solve the puzzle and figure out the sum.

6,864Pool Forum VIP4,114mod280Pool ProSince 2016=32*9*7, you can solve the problem mod 32, mod 9, and mod 7, then use the chinese remainder theorem to find mod 2016.

For mod 32, even values of i are 0, odd ones are 1. Then 2016/2 mod 32 = 16.

For mod 9, values of i divisible by 3 are 0, the rest are 1. Then 2016*2/3 mod 9 = 3.

For mod 7, values of i divisible by 7 are 0, the rest are 1. Then 2016*6/7 mod 7 = 6.

Then combine with CRT to get 48 as the solution for mod 2016.

4,114mod