Advent calendar 2022
18 December
Noel writes the integers from 1 to 1000 in a large triangle like this:
| | | | 1 | | | |
| | | 2 | 3 | 4 | | |
| | 5 | 6 | 7 | 8 | 9 | |
| 10 | 11 | 12 | 13 | ... | | |
The number 12 is directly below the number 6. Which number is directly below the number 133?
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The rightmost entry in the \(n\)th row is \(n^2\). A number below a number in the \(n\)th row is \(2n\) larger than the number in the \(n\)th row.
The smallest square number larger than 133 is 144, so 133 is in the 12th row. This means that the number under it will be 24 greater than it: 133+24=157.
