Question 11 of 48advanced🔍 AnalyzeShort Answer3 marks

Place the numbers 1–6 in the blanks in such a way that the sum on each side of the triangle is 9. No numbers should be repeated.

Correct Answer

Understanding: Corner numbers are counted twice (once for each adjacent side).

Step 1: Total of all numbers = 1 + 2 + 3 + 4 + 5 + 6 = 21

Step 2: Total of three sides = 9×39 \times 3 = 27

Step 3: Difference = 27 − 21 = 6 (sum of corner numbers)

Step 4: Find three numbers that sum to 6: 1 + 2 + 3 = 6

Step 5: Place 1, 2, 3 at corners; place 4, 5, 6 in middle positions.

Answer: One possible arrangement: Corners: 1, 2, 3 Between 1 and 2: place 6 → 1 + 2 + 6 = 9 Between 2 and 3: place 4 → 2 + 3 + 4 = 9 Between 3 and 1: place 5 → 3 + 1 + 5 = 9

∴ Each side sums to 9.

Exercise: Let Us Play | Q: 12 | (Page Page 6)
For More Understanding

Explanation

This puzzle requires placing numbers 1-6 on a triangle such that the sum of numbers on each side equals 9. The corner numbers are counted twice (once for each adjacent side). Students need to find which numbers work as corner numbers and which work as middle numbers.

Solution Steps

  1. Step 1: Identify that corner numbers are counted twice

  2. Step 2: Total of all numbers 1+2+3+4+5+6 = 21

  3. Step 3: If each side sums to 9, total of three sides = 27

  4. Step 4: Difference = 27-21 = 6, which equals sum of corner numbers

  5. Step 5: Find three numbers that sum to 6: 1+2+3 = 6

  6. Step 6: Place 1, 2, 3 at corners, remaining numbers 4, 5, 6 in middle positions

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