Question

Day 1

$\Large\mathsf\red{ Logical \: Challenge:-}$

A sack contains 4 different coloured balls,

14 balls are not blue.
16 balls are not yellow.
24 balls are not red.
12 balls are not pink.

How many balls are there in the sack?

Note:- It may be solved by little bit of math. I mean it is not pure logical.​

Answer 1

$\huge\color{purple}{\mid{\fbox{\tt{Question}}\mid}}$

• A sack contains 4 different coloured balls,
• 14 balls are not blue.
• 16 balls are not yellow.
• 24 balls are not red.
• 12 balls are not pink.
• How many balls are there in the sack?

$\huge\color{pink}{\mid{\fbox{\tt{Solution}}\mid}}$

Let s be the number of balls in the sack, and let the colors be b (blue), y yellow, r red, and p pink. Then we have:

s = b + y + r + p

14 = s – b

16 = s – y

24 = s – r

12 = s – p

Summing the last four equations gives:

66 = 4s – b – y – r – p

66 = 4s – (b + y + r + p)

66 = 4s – s

66 = 3s

22 = s

It would seem there are 22 balls in the sack. But does this answer actually make sense? Let’s check by solving for each color:

______________________________________

14 = s – b

14 = 22 – b

b = 8

______________________________________

16 = s – y

16 = 22 – y

y = 6

______________________________________

24 = s – r

24 = 22 – r

r = -2

______________________________________

12 = s – p

12 = 22 – p

p = 10

______________________________________

But , how can r = -2? The number of red balls should be a non-negative number, so this answer does not make any sense!

There cannot be 22 balls in the sack. The correct answer is there but there is no solution to the given conditions