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If the pattern shown is continued, what number will appear directly below $400$?

$1$
$2$   $3$    $4$
$5$    $6$   $7$    $8$    $9$
$10$  $11$  $12$  $13$  $14$  $15$  $16$

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.