Math, asked by belipaul4567, 2 months ago

Nine pair of boys and girls have bern assigned numbers 1 to 18. Pair two numbers together in such a manner that:
1. The sum of each pair is a square.
2. Number is left out being unpaired.
3. What are the paired numbers?
4. What stratrgy did you use to solve this problem?
5. Also write 5 properties of square numbers?​

Answers

Answered by amitnrw
5

Given  :

Nine pair of boys and girls have been assigned numbers 1 to 18

The sum of each pair is a square.

To Find :   the paired numbers

Solution:

9 + 16  = 25

8 + 17 = 25

7 +  18  = 25

6 + 10  = 16

5 +  11 = 16

4  +  12  = 16

3 + 13 = 16

2 + 14 = 16

1 + 15  = 16

These are the above pairs

( 1 , 15) , ( 2 , 14) , (3 , 13) , ( 4 , 12) , (  5, 11) , ( 6 , 10) . (7 , 18) , ( 8 , 17) , (9 , 16)

No one is left out

Strategy used

Maximum sum can be 18 + 17 = 35

minimum sum can be  1 + 2 = 3

Square numbers in between  = 4 , 9 , 16 , 25

Sum of all numbers = 18 * 19/2 =   171  

16 , 17 and 18 can be used to make 25 only

Hence sum = 75

left sum = 171 - 75 = 96

and pair left = 9 - 3 = 6

16 * 6  = 96

hence 6 sixteen pairs  and  3  pairs of 25  is the only possible combination

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