# On Daily challenge problem

I answered this Daily challenge problem correct but was marked as incorrect. I will give a proof for my answer below

Assumptions:

• Capacity of candies of the cup is constant.

• Candies are mixed well, i.e. the concentration of candies is uniform all over the jar.

• Candies which are more concentrated are more probable to be selected if you pick any candy randomly from a mixture.

Let the capacity of the cup be of $x$ candies

After first step:

Total candies in Jar $B$=$600+x$

Number of Red candies = $x$

Number of Green candies = $600$

Concentration of Red candies = $C_{AR}=\frac{x}{600+x}$

Concentration of Green candies = $C_{AG}=\frac{600}{600+x}$

Taking one cup of candies from jar $B$:

Number of Green candies in the cup = $J_G=C_{AG} \times x=\frac{600x}{600+x}$

Number of Red candies in the cup = $J_R=C_{AR} \times x=\frac{x^2}{600+x}$

After second step:

Total number of candies in jar $A$=$800$

Number of Red candies=$N_R=800-x+J_R=800-x+\frac{x^2}{600+x}=\frac{800(600+x)-x(600+x)+x^2}{600+x}=\frac{4800+800x-600x\cancel{-x^2+x^2}}{600+x}=\frac{4800+200x}{600+x}$

Number of Green candies = $N_G=J_G=\frac{600x}{600+x}$

Concentration of Red candies = $C_{BR}=\frac{N_R}{800}=\frac{4800+200x}{800(600+x)}$

Concentration of Green candies=$C_{BG}=\frac{N_G}{800}=\frac{600x}{800(600+x)}$

After third step:

Concentration of Red candies in the mixture = $\frac{C_{AR}+C_{BR}}{2}=\frac{1}{2}(\frac{x}{600+x}+\frac{4800+200x}{800(600+x)})=\frac{1}{2}(\frac{800x+4800+200x}{600(800+x)})=\boxed{\frac{2400+500x}{600(800+x)}}$

Concentration of Green candies in the mixture=$\frac{C_{AG}+C_{BG}}{2}=\frac{1}{2}(\frac{600}{600+x}+\frac{600x}{800(600+x)})=\frac{1}{2}(\frac{4800+600x}{600(800+x)})=\boxed{\frac{2400+300x}{600(800+x)}}$

If you compare the concentrations of both the candies in the last mixture, you can conclude that Red candies are more concentrated than Green candies

$\therefore$ Red candies are more likely to be selected in the fourth step.

Note by Zakir Husain
2 weeks, 6 days ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

Great! @Zakir Husain. I agree with you but shouldn't you report this as a bug?

- 2 weeks, 6 days ago