Below 400
Can you work out which number will appear directly below 400 in this pattern?
Age
14 to 16
Challenge level
Problem
If the pattern below is continued, what number will appear directly below 400?
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1
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2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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12
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13
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14
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15
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16
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If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Note that the number at the end of the $n^\text{th}$ row is $n^2$, so $400$ will lie at the end of the $20^\text{th}$ row.
The row below will end in $21^2$, i.e., $441$, so the number directly below $400$ will be the number before $441$, which will be $440$.