🦘 Math Kangaroo Grade All Felix 1-2 Ecolier 3-4 Benjamin 5-6 Kadett 7-8 Junior 9-10 Student 11-12 ⇄ switch contest
2017 Math Kangaroo

Problem 20

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?

1213
4112
1732
2131
Show answer
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
  1. Try 2 x 2 blocks, focusing on the area around the 7.
  2. The block with 7, 3 (its right neighbour) and the 1, 3 below them gives 7+3+1+3.
  3. That total is 14, larger than any other 2 x 2 block.
  4. So the greatest sum is 14.
Mark: · log in to save