# 325

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## Number

$325$ (three hundred and twenty-five) is:

$5^2 \times 13$

The $1$st positive integer which can be expressed as the sum of two square numbers in $3$ distinct ways:
$325 = 18^2 + 1^2 = 17^2 + 6^2 = 15^2 + 10^2$

The total of all the entries in a magic square of order $5$, after $1$, $(10)$, $45$, $136$:
$325 = \ds \sum_{k \mathop = 1}^{5^2} k = \dfrac {5^2 \paren {5^2 + 1} } 2$

The total number of permutations of $r$ objects from a set of $5$ objects, where $1 \le r \le 5$

The $10$th positive integer after $200$, $202$, $204$, $205$, $206$, $208$, $320$, $322$, $324$ that cannot be made into a prime number by changing just $1$ digit

The $13$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $120$, $153$, $190$, $231$, $276$:
$325 = \ds \sum_{k \mathop = 1}^{13} \paren {4 k - 3} = 13 \paren {2 \times 13 - 1}$

The $25$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $171$, $190$, $210$, $231$, $253$, $276$, $300$:
$325 = \ds \sum_{k \mathop = 1}^{25} k = \dfrac {25 \times \paren {25 + 1} } 2$