# math puzzle with random letters that decode into numbers?

1. A A , B
A A A , C
A A A A , D
A A A A A , E
A A A A A A , F
A A A A A A A , G
A A A A A A A A , H
A A A A A A A A A , I

2. A J A K B
A J A J A K C
A J A J A J A K D
B J A K C
B J B K D
C J D K G

3. C L A K B
D L A K C
G L B K E

4. A J M K A
D J M K D
C L C K M

5. E J E K AM
E J F K AA
AM J AM K BM
CM J B K CB

6. B N C K F
B N E K AM
E N AB K FM
AM N AM K AMM

7. H O B K D
AM O E K B
AMM O BM K E

8. A O AM K PA
A O AMM K PMA
A O B K PE
A O D K PBE

9. C N C K C Q K I
D N D K D Q K AF
AM Q K AMM

10. R AMM K AM
R BE K E
R G Q K G

• -1 I know homework questions are allowed on puzzling but OP does not appear to have attempted any of the questions themselves. I would've at least expected a few guesses. Mr Benson would not be pleased! Jan 5, 2018 at 15:47

From top to bottom:

Case 1

establishes A .. I as the counting system. That is, it tells us they are the digits 1 .. 9.

Case 2

introduces the symbols J and K. All of the lines are satisfied if we interpret J as addition and K as the equivalence predicate (==)

Case 3

introduces L. Expectations from case 2 tell us that L should be subtraction.

Case 4

introduces M. We observe that it's the 0 digit.

Case 5

introduces juxtaposition. It tells us that digits stuck to each other should be interpreted as decimal.

Case 6

introduces N. We would expect to learn multiplication somewhere around this time, and it is indeed the case.

Case 7

introduces O. Previous cases help us recognize the division operator.

Case 8

introduces P. Matching with the division results tell us that P represents the decimal point, perhaps with a zero next to it.

Case 9

introduces Q. It represents the sQuare operator, and it's postfix.

Case 10

introduces R, for square Root, a prefix unary operator. Nice timing, possibly deliberate.

• I had to chuckle that someone named Dvorak is best at interpreting what appears to be jumbled letters. :-) Jan 5, 2018 at 7:21
• @Phylyp You know what's crayz? German keyboards. Jan 5, 2018 at 18:16