Time to bid adieu to 2014

Number Theory Level 4

In place of 1 to 6 dots on a regular dice, some random positive integers are written on all the six faces, one such number on each face. The sum of products of the three numbers on the three faces that meet at each of the eight corners is 2014.

Find the sum of the numbers written.

The answer is 74.

1 solution

Aditya Raut
Dec 16, 2014

One very Awesome question, really loved it.

Let the numbers written on the faces be $a,b,c,d,e,f$ such that

$a$ is opposite to $b$

$c$ is opposite to $d$

$e$ is opposite to $f$

Then, the given sum actually becomes into

$(a+b)(c+d)(e+f) = 2014$

Now because $a,b,c,d,e,f$ are all positive integers, there is only one integer factorization possible and it is $2014 = 2\times 19 \times 53$ .

Because of this, we get that $a+b+c+d+e+f = 2+19+53 = \boxed{74}$

Was on right track till geting factors...didnt thought of adding them.....

Sandeep Gupta - 6 years, 5 months ago

Time to bid adieu to 2014

The answer is 74.

1 solution

0 pending reports