Subject: magic triangles
Name: Sandy
Question: You have the numbers 4, 5, 6, 7, 8, 9. Suppose that the sum on each side were to be 21 instead of 20. The starting clue would be that there are not many ways to use the 4 in a triplet of numbers summing to 21. The only choice is 4 + 8 + 9 = 21. The lower edge of the triangle should be 8 4 9 You cannot put the 4 on a vertex because it cannot be used again in a triplet summing up to 21. Next, where should you put the 5? It cannot be paired with 8, because 8+5 = 13, so 8 more is missing to sum up to 21, and you are not allowed to use that number again. So you must put 5 on the side next to the 9: 5 8 4 9 And now it is easy to complete the triangle: 7 6 5 8 4 9 There is no recipe for such puzzles. Just use your imagination, trial and error, and it will work out. If you are tutoring, provide clues or encouragement when the student is about to give up, but let the student find the solution. Claude
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