Problem:
The numbers , , , , , , and are among the rows, columns, and diagonals of a square grid of digits (rows and diagonals read left-to-right, and columns read top-to-bottom). What 3-digit number completes the list?
Solution
Solution:
| 1 | 1 | 2 |
|---|---|---|
| 5 | 2 | 4 |
| 3 | 1 | 3 |
The center digit is the middle digit of 4 numbers (hence at least 3 members of the above list), so it must be . The top-left digit begins at least 2 members of the above list, so it must be or . If it is , then after placing we see that we need three more numbers starting with , impossible; hence, it is . So and must (in some order) be the last row and the last column, and now it is easy to complete the grid as shown; the answer is .
Want a route through all this instead of an archive? The track
puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.