Grades 5-6 Video Solutions 2023-2023_1-2

Video Transcription

Question 26. Martin has three cards with numbers written on both sides.  The card with number 1 on one side has number 4 on the opposite side.  The card with 2 on it has 5 on the opposite side.  And the card with 3 on it has 6 on the opposite side.  Martin randomly places all three cards on the table and adds up the three numbers he sees. How many different sums can Martin get?  Let's start off by assuming all the cards ended up on the front side.  So we get 1 plus 2 plus 3, which would give us 6.  Next, let's say instead of 1 we had a 4.  This would give us a sum of 9.  Next, if instead of 2 we had a 5, we would get 9 again.  So this would not be a different sum.  And likewise, if instead of 3 we had 6, again we'd get 9. So this would not be a different sum.  Next, let's say we had 4, 5, and 3. This would give us 12.  If we had 4, 2, and 6, that would also be 12. So not a different sum.  And if we had 4, 5, and 6, all cards on the back, we would get a sum of 15.  With this, we've gone through every example of combinations that we could get. This gives us our answer, which would be b, 4 different sums.

Video Summary

Martin can achieve four different sums with his cards. By flipping different cards, the possible sums are 6 (front sides: 1, 2, 3), 9 (mixed sides), 12 (mixed sides), and 15 (back sides: 4, 5, 6). These combinations are thoroughly considered in the analysis of different arrangements.