Sunday Times Teaser 2088 – Black and White
by Adrian Somerfield
Published 22nd September 2002
Throughout the following calculations, each digit has consistently been replaced by a letter, with different letters for different digits:
BL / WH – AC / IT = K / E
Here the fractions are not necessarily in their simplest form — indeed, each of the three fractions in the above subtraction is in fact a whole number. Furthermore (though you might not need to know all these):
IT / WB + CA / KL = H / E
WB / TI x KL / CA = E / H
BT / IK ÷ EL / WA = H / C
What number is BLACK?
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It seems you haven’t checked the last equation (or prevented division by zero for C).
There is no need to do either because the solution is unique without these
checks (it can be shown that C cannot be zero because L must be). We are
also told that we might not need all the equations and so it turns out.
I forgot about “though you might not need to know all these”. Still you only know that you don’t need the last equation untill you have run the program.