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Good Math by Mark C. Chu-Carroll

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Puzzling Symmetry

Let’s play a game that I’m calling crypto-addition. I’ve taken the letters a through k and I’ve assigned each one to one of the numbers between -5 and +5, and I want you to figure out which letter represents which number. The only clues come from Table 3, A crypto-addition table, where I’ve shown you the sums of different letters whenever that sum is between -5 and +5.

Table 3. A crypto-addition table

The letters a through k represent the numbers between -5 and +5. Entries in the table represent the sums of the row and column labels.

abcdefghijk
a: bah f dk
b: fbd kach
c:bfgcikjd eh
d:abcdefghijk
e:hd e c j g
f: kfc hbgda
g:fkje hec id
h: adhjbckegf
i:dc i g e j
j:k1ej dig c
k: hkgadfjcb

Using the crypto-addition table, what ...

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