Grades 3-4 Video Solutions 2024-2024_3-4

Video Transcription

Question 13. Seven cards, numbered 1 to 7, are placed in four overlapping rings. The sum of the numbers in each ring is 10. Which number is under the question  mark? Let's start off by drawing our diagram of four circles and seven cards. Now we know that each of the circles ends up with a sum of 10. So let's take  a look at the two circles that only have two cards each. First we have the circle on the very left, which has a card with a 6 and an unknown. To get the  sum of 10, we will put in 4. On the other side we have the circle with a blank and a 3. Here we put in 7. Let's return the other two circles and since  there are cards that are 1 to 7, all the numbers are different. What we are missing are numbers 1, 2, and 5. Let's get rid of these side circles so as to not  worry about them. First let's place the 5. The 5 cannot go on the second or the third card, because if we add it to 7 it will be 12 plus a number, which would be  a sum over 10. So the 5 has to go here. Next we will put the 2 here, because the only other number that is left is 1, and it ends up with a sum of 10 for both  circles. 4 plus 5 plus 1 is 10, and 1 plus 2 plus 7 is 10. So the answer will be A, 1.

Video Summary

The problem involves seven numbered cards arranged in four overlapping rings, with each ring summing to 10. The process begins by addressing two rings with partial information—one with 6 and a blank requiring a 4, and another with 3 and a blank needing a 7, to complete sums of 10. Remaining numbers 1, 2, and 5 are then distributed among the other circles. The 5 cannot be placed in certain positions as it would exceed the ring sums, eventually leading to the placement of 1 where it satisfies the conditions for all rings. The solution is the number 1.