These are many unknowns

Logic Level 2

Solve the cryptogram

X J C P P + X D E N K C J B Q B C \large{\begin{array}{cccccccc} &&&X&J&C&P&P \\ +&&&X&D&E&N&K \\ \hline &&C&J&B&Q&B&C \\ \end{array}}

and find the value of X + J + C + P + D + E + N + K + B + Q X+J+C+P+D+E+N+K+B+Q .

I'm sorry for not finding valid words for this; if someone can come up with some, I would love to see them.


The answer is 45.

Henry U by Henry U , 17, Germany

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3 solutions

If each letter is a distinct digit, there are 10 distinct digits. Therefore, the sum is 0 + 1 + 2 + 3 + 4 + ... + 9 = 45

2 Helpful 0 Interesting 1 Brilliant 0 Confused
Winston Choo
Jan 4, 2019

Well, the problem asked us to solve the cryptogram, so here it is:

62144 + 65937 = 128081

It is now obvious that the sum all of the distinct letters is 45.

1 Helpful 1 Interesting 0 Brilliant 0 Confused

I had thought of the solution 62188 + 67403 = 129591 62188+67403=129591 , so it looks like there are more than one, and that's also a reason why I asked for the sum of all lettees.

Henry U - 2 years, 5 months ago

There is a total of 5 solutions: 

1
2
3
4
5
 
62188+67403=129591
74155+73926=148081
62144+65937=128081
62144+63807=125951
87122+86409=173531

Pi Han Goh - 2 years, 5 months ago

Thanks! I find it interesting how some solutions have numbers in common, and that 621 for XJC gives three otherwise different solutions.

Henry U - 2 years, 5 months ago

Then the answer we must ask should be not the sum of all digits, but the minimal sum for example.

Hasmik Garyaka - 2 years, 4 months ago
Jordan Cahn
Jan 4, 2019

There is no need to solve the cryptogram since each letter represents a distinct digit. 0 + 1 + 2 + ⋯ + 9 = 45 0+1+2+\cdots+9 = \boxed{45} .

1 Helpful 0 Interesting 1 Brilliant 0 Confused

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