Question

NATIONAL MATHEMATICS DAY SPECIAL CHALLENGE

A teacher has 25 apples each numbered from 1 to 25. He wants to distribute the apples between his students in such a way that the sum of numbers written on the apples distributed among the 5 students are same.

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Answer 1

Required Answer:-

Question:

• A teacher has 25 apples each numbered 1 to 25. He wants to distribute the apples between his student in such a way that the sum of numbers written on the apples distributed among the 5 students are same.

To find:

• The apple numbers which each student get.

Solution:

Since the apples are numbered 1 - 25, sum of those numbers will be,

S = 1 + 2 + 3 + 4 + ..... + 25

Here,

➡ a = 1

➡ d = 1

➡ n = 25

So,

Sum,

= 25/2[2 × 1 + (25 - 1) × 1]

= 25/2[2 + 24]

= 25/2 × 26

= 25 × 13

= 325

So, sum of all the numbers is 325

As there are 5 students, so sum of numbers in apples of each student will be,

= 325/5

= 65

Now, find out the magic square constant for 5x5 square.

➡ n = 5

Magic Square Value = n(n² + 1)/2

= 5(25 + 1)/2

= 5 × 26/2

= 5 × 13

= 65

➡ Now, let us fill the 5x5 square by using numbers from 1 - 25 such that sum of all the numbers (row wise or column wise) is 65.

See the attachment for the table.

These are the number values in apples of each student.

If you rotate the table once, you will get another combination which is also a solution to the question.

You can check it.

1. 17 + 24 + 1 + 8 + 15 = 65
2. 23 + 5 + 7 + 14 + 16 = 65
3. 4 + 6 + 13 + 20 + 22 = 65
4. 10 + 12 + 19 + 22 + 3 = 65
5. 11 + 18 + 25 + 2 + 9 = 65