Problem 20 · 2017 Math Kangaroo
Stretch
Arithmetic & Operations
gridcareful-counting
A number is written into every square of a 4 × 4 table. Mary is looking for the 2 × 2 table where the sum of the four numbers is greatest. How big is this sum?
| 1 | 2 | 1 | 3 |
| 4 | 1 | 1 | 2 |
| 1 | 7 | 3 | 2 |
| 2 | 1 | 3 | 1 |
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Answer: D — 14
Show hints
Hint 1 of 2
Slide a 2 x 2 window over the table and add its four numbers each time.
Still stuck? Show hint 2 →
Hint 2 of 2
The biggest entry, 7, should sit inside the best window.
Show solution
Approach: check the 2 x 2 block containing the largest numbers
- Try 2 x 2 blocks, focusing on the area around the 7.
- The block with 7, 3 (its right neighbour) and the 1, 3 below them gives 7+3+1+3.
- That total is 14, larger than any other 2 x 2 block.
- So the greatest sum is 14.
Mark:
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