Ode to the EU & the UK

Logic Level 3

E U × U K N O P E \begin{array}{ccccc} & & & & E&U\\ \times & & & & U & K \\ \hline & & N & O & P &E\\ \hline \end{array}

The above shows a cryptogram representing the product of two 2-digit integers to produce a 4-digit integer. Given that each letter represents​ distinct digits, and O = 4 O =4 , what is the value of the 4-digit integer N O P E ‾ \overline{NOPE} ?


The answer is 5418.

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Wee Xian Bin by Wee Xian Bin , 25, Singapore

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1 solution

Kushal Bose
Jun 29, 2016

(10E + U)(10U+K)=100EU+10EK+10U*U+UK=1000N + 400 +10P +E

So, UK-E is divisible by 10

Now Vary E fro 1 to 9 and it csn be easily get a pairs of U and K

Some pairs can be filtered with the condition of distinct digits.

If E=8 then UK=18 It can be esily verify U=6 and K=3

Hence NOPE=5418

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