You have six boxes numbered 1, 2, 3, 4, 5 and 6 respectively. Your friend has distributed n balls among these boxes. What is the smallest value of n for which you can guarantee that there is at least one box that contains at least as many balls as the square on the number written on it?
Answers
Answer:
(B) The number of ways in which 1 green ball can be put
=
6
. The number of ways in which two green balls can be put such that the boxes are consecutive
= 5
(i.e.,(1,2),(2,3),(3,4),(4,5),(5,6))
Similarly, the number of ways in which three green balls can be put
=
4(i.e.(1,2,3),(2,3,4),(3,4,5),(4,5,6))
⋯⋯⋯⋯⋯
and so on.
∴
Total number of ways of doing this
=
6+
5+
4+
3+
2+
1=
21
Answer: 86
Step-by-step explanation:
First Box_(1) square number = 1
Second Box_(2) square number = 4
Third Box_(3) square number = 9
Fourth Box_(4) square number = 16
Fifth Box_(5) square number = 25
Sixth Box_(6) square number = 36
Now,
subtracting 1 from the square numbers then adding them, we get,
0+3+8+15+24+35
= 85
Now, if we give 1 ball to any box then we can guarantee at least 1 box with the square number of balls.
then, n = 85+1
=86