# Strange Calculator

I found this Strange Calculator, and I don't know how it works.

This is what it looks like:

I've run some problems through it and here are the results:
$$\begin{array}\ &A+B = 23 & F-G = -1 & K\times L = 156\\ &B+C = 25 & G-H = -1 & L \times M = 182\\ &C+D = 27 & H-I = -1 & M \times N = 210\\ &D+E = 29 & I-J = -1 & N \times O = 240\\ &E+F = 22 & J-K = -1 & O \times P = 128\\ \\ &\frac{P}Q = 0.8888888888888888 & \frac{Q}R = 0.9&\\ &\frac{R}S = 0.9090909090909091 & \frac{S}T = 0.9166666666666666&\\ &\frac{T}U = 0.9230769230769231 \\ \\ &U^V = 3937376385699289 & V^W = 155568095557812224&\\ &W^X = 6568408355712890625 &X^Y = 295147905179352825856&\\ &Y^Z = 118587876497 \\ \end{array}$$

EDIT corrected precision issue. Thanks to @f'' !

If I need to supply more calculations, let me know what you'd like! (One per customer, please)

I'd like to know:

What values do the letters represent?
How were they derived?

I had a link to the actual Flash Calculator, and wanted to supply it to you so that you could do your own experiments, but I can't find it right now.
Maybe It'll turn up eventually...

A=11
B=12
C=13
D=14
E=15
F=7
G=8
H=9
I=10
J=11
K=12
L=13
M=14
N=15
O=16
P=8
Q=9
R=10
S=11
T=12
U=13
V=14
W-Z seem to be slightly different. Working on it!

Not sure how they were derived yet, just noticed that:

P/Q = 8/9, and 128 is divisible by 8. The rest I worked out from there

Courtesy of f'' (last few and derivation)

W=15
X=16
Y=17
Z=9
Each is the sum of the digits in the decimal ASCII value for the capital letter

• WXY are 15-17, but the calculator must have run out of precision. – f'' Jun 13 '16 at 14:47

A=23-B C=25-B......K=B L= 156/B and M=7B/6

Now B should be Multiple of 6

Going further N=180/B Now B should be factor of 180 and multiple of 6 So B could be (6,12,18,30,45 or 90)

P=96/B Now B should be factor of 96 and multiple of 6 So now the remaining possible values of B are 6 or 12

Values of B are B=6 or B=12

Going further Q would be 9 (if B is 12) or 18(if B is 6) R would be 10 or 12... U would be 13 or 26 Now V can be derived only from 13 not from 26. So we can easily ignore B=6

Now the final value of B = 12 and rest of the values are given below.

A=11 C=13 D=14 E=15 F=7 G=8 H=9 I=10 J=11 K=12 L=13 M=14 N=15 O=16 P=8 Q=9 R=10 S=11 T=12 U=13 V=14 W=15 X=16 Y=17 Z=9