  ## Problem

What is the logic?

### Related Question

You are given the following equation
SUN + SUN + SUN + SUN + SUN + SUN = BRU
where each letter stands for a digit.
The value of SUN is

You are given the following equation
SUN + SUN + SUN + SUN + SUN + SUN = BRU
where each letter stands for a digit.
The value of SUN is

Hi Aniruddha,

It's not a surprise that you are confused. This is a very difficult question for your grade.  The reason we did put it for your grade is that you already have the required knowledge to solve it, all you need is to think in the right direction.

Kudos for trying it.

Let's see what we know. From the question, we know the following

• Both SUN and BRU are 3 digit numbers.
• The middle digit of the first one is the last digit of the 2nd one. The other digits are different from each other
• From the equation above, we can see 6 x SUN = BRU

Now we need to apply logic to see if we can solve it. Let's see what we can figure out

Hmm..."S" cannot be more than 1, because if it was then 6 X SUN would be 4 digits i.e. even the smallest value of SUN in that case would be 201, and  201 x 6 = 1206. But we know that  6 x SUN is 3 digits.

So S = 1
For the same reason U cannot be more than 6 (170 x 6 is 4 digits)

Now think about N.  Can it be even?

No - it cannot. And why?

Think about it  - 6 multiplied by any even number results in the same last digit (6X2 = 12, 6X4 = 24, 6X6 = 36 and so on). But we know that the last digits of SUN and BRU are different.

So N is odd. It can't be 1 though, because S=1
So it's either 3,5,7 or 9

It cannot be 3, because 3x6 = 18. This means U is 8, and we already know U is not greater than 6

Now it's just a matter for elimination.

The possibilities are

N=5 and U = 0

N = 7 and U = 2

N = 9 and U = 4

Now you have 3 possibilities for SUN (105, 127 and 149). It is easy enough to multiply them by 6 and seeing which one results in the right possibility.

EduGain Team

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