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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.*