# Find the missing number: 321,6; 432,48; 333,81; 432,353; 321,?

Looking for the solution of IQ question below:

321 6
432 48
333 81
432 353
321 ? • [POTENTIAL SPOILER] A pattern for the first three rows: left column cell product multiplied by row index = right column cell. 3*2*1*1 = 6, 4*3*2*2 = 48, 3*3*3*3 = 81. But then for the fourth row, 4*3*2*4 = 96 != 353. :/ Also, 353 is a prime number. – SpiritFryer Jul 13 '16 at 3:40
• Where is the image from? – f'' Jul 13 '16 at 5:48
• Just for clarity. Are you asking for the solution of the question, or asking how one goes about to solve such a question? Your first line is slightly confusing here and might require an edit... – BmyGuest Jul 13 '16 at 6:32
• Also noted the 4^4 + 3^4 + 2^4 = 353 – Maxqueue Jul 13 '16 at 15:56
• I had this as an answer until z100 pointed out it was wrong: going off of @Maxqueue's comment, we see that $3^1+2^1+1^1=6$, $3^3+3^3+3^3=81$, and $4^4+3^4+2^4=353$, but $4^2+3^2+2^2=29\neq 48$. – DooplissForce Jul 13 '16 at 16:42

(Yielding $276$)

- basically fudging it with what people have noted in the comments...

The number on the left has digits
$d_nd_{n-1}\cdots d_2d_1$
and is in row $r$, starting at $1$

The number on the right is whichever of $$A=\sum_{i=0}^n{d_i^r}$$ $$B=d_n^rd_{n-1}$$ is smaller after its digits have been reversed.

That would be

If $x'$ reverses the digits of $x$

Row  Left     A     B     A'    B'   min(A', B')' = Right
1   321     6     6     6     6              6
2   432    29    48    92    84             48
3   333    81    81    18    18             81
4   432   353   768   353   867            353
5   321   276   486   672   684            276

Not really fitting for an "IQ" test though.

Kind of reaching a little here but here goes:

if index is prime apply following pattern where n is the index and d is the digit:dxdxdxn If index is not prime apply following pattern where n is the index and d is the digit:d^n + d^n + d^n Therefore the answer would be: If index is prime apply following pattern where n is the index and d is the digit:dxdxdxn

30

Because of the fact that:

the index is 5 which is prime so 3x2x1x5=30

• The number 1 isn't prime. – dpwilson Jul 13 '16 at 16:46
• @dpwilson Still works, since $3^1+2^1+1^1=6$. :) – DooplissForce Jul 13 '16 at 16:48
• @dpwilson: Yes, but 1·2·3·1 and 1¹ + 2¹ + 3¹ are both six. – M Oehm Jul 13 '16 at 16:48
• Ha, whoops. My bad. – dpwilson Jul 13 '16 at 16:48
• I hope there is a cleaner solution (I don't like the change of pattern with prime numbers) – Fabich Jul 13 '16 at 20:39

276

because you can get right hand side choosing

$$\max \left \{ nabc, a^n+b^n+c^n\right \}$$where $n$ is number of the row starts from $1$