Question number 22. In the picture to the right, each animal represents a positive integer, and different animals represent different integers. The sum of the two integers in each column is written below that column. What is the largest possible sum of the four integers in the first row? Let's start with column number 3. But before that, let's first look and see that every single animal over here is different. So all of these numbers, that means, are all different. So we have column number 3. The only way to get a sum of 3 with two distinct integers is with values 1 and 2. Now, of course, we want the largest number on the top to make the largest possible sum on the top, so 2 is the one that should be on top, and we have 1 in the bottom. And then moving on to the fourth column, since 1 and 2 have been used, the only values that we can now use are 3 and 4. Again, we'll have 3 in the bottom row, and then 4 in the top row to increase the sum. For column 2, the values are 5 and 6, because now 1, 2, 3, and 4 have all been used. 5, in this case, will be on the bottom row, and 6 will be on the top. And for column 1, the values are going to be 7 and 8, since numbers 1 to 6 have been used. So 7 is going to be on the bottom, and 8 is going to be on the top. That means that our total values are going to be 2 plus 4 plus 6 plus 8. And that sums up to 20, so the answer is C.

integer assignment

distinct integers

column constraints

maximize sum

animal puzzle