If there are exactly two white balls, then which one of the following boxes could contain a green ball?

Irina on August 5 at 01:27AM

@ ali,

The setup for this game is fairly straightforward even though there are few initial deductions:

We have six boxes with one ball each, either g, r, or w

___ ___ ___ ___ ___ ___
1 2 3 4 5 6

(1) There are more red balls than white

R >W

(2) There is a box containing a green ball that is lower than any box that contains a red ball

G(1) -> R

What this rule is telling us is that there is at least 1 green ball that is below all the red ones. There could be more green balls that are above red ones, hence we cannot rule out box #6 as not green, but we can conclude that box #1 is not red.
___ ___ ___ ___ ___ ___
1 2 3 4 5 6
~R

(3) There is a white ball in a box that is immediately below a box with a green ball.

WG

Now, the question asks us if we have two white balls, then which one could contain a green ball?

Let's think about this setup:

Per rule (1), if we have 2 W, 3R, and 1G ball. Per rules (2) and (3) we can conclude that this G ball must be below all the R balls, and directly above the W ball.

/R
/G /G /W /W /W
W /W /W R R R
___ ___ ___ ___ ___ ___
1 2 3 4 5 6


These restrictions demonstrate that the lowest possible box for the G ball could be #3 if all 3 R balls are consecutive and are in boxes #3, #4 and #5.

W W G R R R
___ ___ ___ ___ ___ ___
1 2 3 4 5 6


The only other alternative for the G ball is the box #2 in a scenario where boxes 3,4,5, and 6 are filled with some combination of 3 red and 1 white ball, the exact order of which is not restricted by any of the rules Box #1 must be the W ball per rule (3).

/R /W /W /W
W G /W /R /R / R
___ ___ ___ ___ ___ ___
1 2 3 4 5 6

Does this make sense?

Let me know if you have any further questions.

Madeline on May 20 at 07:01PM

The maximum amount of R's could be four, can't the minimum be two? For example WGRRGG or WGRGRG or GRRGWG, etc.

Ben on May 31 at 03:12AM

Hi Crook, thanks for reaching out.

You are right. The maximum R's is 4 and the minimum is 2. There are multiple ways we can have 2 Rs. The ones you have shown are acceptable.

Keep up the good work!