# Mathematical alphabetical equation

Assume that the following three equations hold true:

• $C \circ I \circ D \circ A = B$
• $O \circ K \circ M \circ G = C$
• $Y \circ A \circ B \circ C = D$

Find the right hand side of the following equation:

• $S \circ W \circ A \circ G =~ ?$

Hints:

1.

Convert each letter to its corresponding numerical value.
E.g., $C \circ I \circ D \circ A = B$ is converted to $3 \circ 9 \circ 4 \circ 1 = 2$

2.

Use mathematical operators to make above equations work out.

3.

All the equations follow the same pattern. Just find a pattern, apply it to the last equation and find the result.

• There is hardly any overlap between the letters in each equation, which means it is trivial to assign values to each letter and make S + W + A + G equal whatever you want. – GentlePurpleRain Nov 22 '15 at 5:48
• @GentlePurpleRain, Yes.... there is a logic to solve this puzzle. This is an interview question. I took almost half an hour to solve it and of course after getting a hint.. – H.Modh Nov 22 '15 at 6:25
• Hint: Convert each alphabet to its corresponding numeric value...!! Then solve it using mathematical operators. – H.Modh Nov 22 '15 at 7:12
• Would the question be more accurate if listed as $f(S,W,A,G)=?$ or is the usage of three operators significant? – Ian MacDonald Nov 23 '15 at 17:34
• Do the letters map to unique numbers (e.g. $B=2 \implies C \ne 2$)? Do all the circles represent the same operation (e.g. all multiplications, or all additions, etc)? – Lawrence Nov 24 '15 at 4:10

$S \circ W \circ A \circ G = G$

Explanation: After plugging in the values $A=1,~B=2,~C=3,~\ldots,~Z=26$, each of the three example equations $~~~\alpha\circ\beta\circ\gamma\circ\delta=\epsilon~~~$ follows the pattern

$~~~(\alpha+\beta)/\gamma+\delta=\epsilon^2~~~~~$ respectively $~~~~~\epsilon=\sqrt{(\alpha+\beta)/\gamma+\delta}$

Indeed, the three given equations give us the following:

    C o I o D o A = B    yields     3 o  9 o  4 o  1 = 2
O o K o M o G = C    yields    15 o 11 o 13 o  7 = 3
Y o A o B o C = D    yields    25 o  1 o  2 o  3 = 4


One easily verifies that

$(3+9)/4+1=2^2~~~$ and $~~~(15+11)/13+7=3^2~~~$ and $~~~(25+1)/2+3=4^2$

$S\circ W\circ A\circ G=G~~~~~$ as $~(19+23)/1+7=7^2$