Almost Nothing Is Given

Logic Level 1

$\large{\begin{array}{ccccccc} && & & & & \square & 2\\ \times && & & & & \square &4\\ \hline & & & & \square & \square & \color{#D61F06}\square &8\\ \hline \end{array}}$

The above shows an incomplete long multiplication. Each square represents a distinct non-zero digit other than 2, 4, and 8 already used in the long multiplication. What is the value that represents the red square?

3 5 6 7

5 solutions

Harry Alderson
Jul 28, 2016

Red box = 4* top left(x) + 2*bottom left(y). Therefore r = 4x + 2y. The only numbers that fit on the options is 6 as it is the only even number.

Wen Z
Jul 16, 2016

Relevant wiki: Cryptogram

Firstly, $52 \times 34 =1768$ works.

Now observe that since the digit is even as it is congruent to 2a+4b mod 10, it has to be 0, 2, 4, 6 or 8. However it cannot be 2, 4 or 8 since the digits are distinct and it cannot be 0 as the digits are non-zero, hence the answer is 6.

Thank you for your solution!

Pi Han Goh - 4 years, 11 months ago

Prateek Gupta
Jul 15, 2016

It's obvious that 6 will come as the other options cannot appear if we multiply anything by 4.

Prince Loomba
Aug 13, 2016

x2×y4

(4x)8

(xy)(2y)0

This gives the second last digit of the answer as unit digit of 2y+4x, which is surely even. Only 6 satisfies

Romain Milon
Jul 16, 2016

The next digit will be a multiple of $2 (mod 10)$ . Among the proposed solutions, only 6 can fulfill this condition.

Almost Nothing Is Given

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