Samacheer Kalvi Class 6 Maths Solutions Term 1 Chapter 6 Information Processing Exercise 6.2

Question 1. In the following magic triangle, arrange the numbers from 1 to 6, so that you get the same sum on all its sides.
Answer: The numbers from 1 to 6 can be placed in the circles of the triangle as shown in the diagram below. Each side of the triangle will then add up to the same total. For this specific arrangement, each side sums to 9 (for example, 1+5+3=9). This type of puzzle makes numbers combine in a special way.
In simple words: You need to place numbers 1 to 6 in the circles on the triangle so that if you add the numbers on any side, you get the same total. The picture above shows one way to do it, where each side adds up to 9.

🎯 Exam Tip: When solving magic shape puzzles, it's helpful to first identify the number of positions and the range of numbers allowed. Start by trying smaller numbers in corner positions and larger ones in the middle, or vice-versa, to balance the sums.

Question 2. Using the numbers from 1 to 9
(i) Can you form a magic triangle?
(ii) How many magic triangles can be formed?
(iii) What are the sums of the sides of the magic triangle?
Answer:
(i) Yes, it is possible to form a magic triangle using the numbers from 1 to 9.
(ii) There are 5 different magic triangles that can be formed using these numbers. This shows that there can be multiple solutions for such puzzles.
(iii) The possible sums for the sides of these magic triangles are 17, 19, 20, 21, and 23. This means that depending on how you arrange the numbers, you can achieve different constant sums for each side.
In simple words: Yes, you can make a special triangle with numbers 1 to 9 where each side adds up to the same number. You can make 5 different kinds of these triangles, and the numbers on their sides can add up to 17, 19, 20, 21, or 23.

🎯 Exam Tip: For problems asking about the existence and properties of magic shapes, remember that more numbers often lead to more possible solutions and different potential sums. A full set of numbers (like 1 to 9) can be arranged in many ways.

Question 3. Arrange the odd numbers from 1 to 17 without repetition to get a sum of 30 on each side of the magic triangle.
Answer: The odd numbers from 1 to 17 are 1, 3, 5, 7, 9, 11, 13, 15, 17. Six of these numbers can be arranged in the circles of the magic triangle as shown below. This arrangement helps in fulfilling the properties of a magic triangle using specific odd numbers. The goal is for the numbers along each side to add up to 30.
In simple words: Take some odd numbers from 1 to 17, and put them in the triangle circles so each side adds up to 30. The picture above shows one way to place the numbers.

🎯 Exam Tip: When working with odd numbers, remember their properties: the sum of three odd numbers is always odd. If the target sum is even (like 30), ensure your number selection and placement logic can achieve it, perhaps by using numbers strategically in corners and midpoints.

Question 4. Put the numbers 1, 2, 3, 4, 5, 6 & 7 in the circles so that each straight line of three numbers add up to the same total.
Answer: The numbers 1, 2, 3, 4, 5, 6, and 7 can be arranged in the circles of the star shape as shown in the diagram below. The central number is 7, and the other numbers are placed on the outer points. The arrangement ensures that the numbers along certain straight lines add up to a consistent sum.
In simple words: Place numbers 1 to 7 in the circles of the cross shape. The number 7 goes in the middle. The other numbers go around it, so that if you add any three numbers in a straight line, they should give the same total.

🎯 Exam Tip: When placing numbers in a star or cross shape, the central number often plays a key role in balancing the sums of the radiating lines. Experiment with different central numbers first if the problem allows.

Question 5. Place the number 1 to 12 in the 12 circles so that the sum of the numbers in each of the six lines of the star is 26. Use each number from 1 to 12 exactly once. Find more possible ways?
Answer: One way to arrange the numbers from 1 to 12 in the 12 circles of the six-pointed star, such that the sum of the numbers in each of the six straight lines is 26, is shown below. This is a classic magic star puzzle. For example, the top horizontal line sums to 1 + 6 + 8 + 11 = 26. Other arrangements are possible too. The goal is to use each number exactly once.
In simple words: You need to fill the star with numbers from 1 to 12, using each number once. The goal is that when you add the four numbers along any of the six straight lines that make up the star, the total should be 26. The picture above shows one way to do this.

🎯 Exam Tip: Magic star puzzles require careful placement and checking. Start by placing numbers in a pattern and then systematically check the sums of the lines. There can often be several valid arrangements, so explore different possibilities.