Problem number 18. Seven cards are arranged as shown. Each card has two numbers on it, with one of them written upside down. The teacher wants to rearrange the cards so that the sum of the numbers in the top row is the same as the sum of the numbers in the bottom row. She can do this by turning one of the cards upside down. Which card must she turn? A, card A. B, card C. C, card D. D, card F. Or E, card G. In order to know how to change the sums, we first need to find the sums in the top row and in the bottom row. In the top row we have 7 plus 8, that's 15, and 5 more, that's 20. And then we have 4 plus 2, that's 6, that's 26. 3 and 2 is 5 more, so 26 plus 5 is 31. In the bottom row, we have 5 plus 5, that's 10. 3 and 7, that's another 10, so that's 20. 7 plus 4 is 11, so that's 31. And 4 more makes 35. Now the difference between the two sums right now is 35 minus 31, which is 4. We're going to be changing both sums by flipping the cards. We're not going to change one of the sums by 4. Instead, we will need to split this difference in half, so that becomes 2. We will need to add 2 to the top sum and subtract 2 from the bottom sum, which would then give us 33 in both rows. Now we need to find a card where the difference between the numbers is 2 with the smaller number being on top. The first card has the bigger number on top, so that will not be the card we flip. B has a difference of 2. 5 minus 3 is 2, but the bigger number is on top, so that's still not it. C has a difference of 1. 5 minus 4 is 1, so it doesn't work. In D, it's 5 minus 2 is 3. That also doesn't work. In E, the difference is 8 minus 7. That doesn't work. In F, 7 minus 3 is 4, which is not what we're looking for. And in G, we have 4 minus 2, which is 2, and the bigger number is on the bottom. If we flip it, we end up with 4 on top, 2 on the bottom, so that increases the top number by 2 and decreases the bottom number by 2, giving us a sum of 33 in both rows. So the answer is E.

card flipping

equal sums

math puzzle

card G

rearranging cards