Let A be a matrix of order 22, whose entries are from the set 0,1,2,3,4,5.

Question

Let $A$ be a matrix of order $2	imes2$, whose entries are from the set $\{0,1,2,3,4,5\}$. If the sum of all the entries of $A$ is a prime number $p$, $2<p<8$, then the number of such matrices $A$ is\_\_\_\_

Answer: 180

Accepted Answer

Possible primes: $p=3,5,7$.

$p=3$: entry patterns $(0,0,0,3),(0,0,1,2),(0,1,1,1)$ give $4+12+4=20$ arrangements.

$p=5$: patterns $(0,0,0,5),(0,0,1,4),(0,0,2,3),(0,1,1,3),(0,1,2,2),(1,1,1,2)$ give $4+12+12+12+12+4=56$.

$p=7$: patterns (per the source) sum to $104$ arrangements.

Total $=20+56+104=180$.

Solutions · 1