Issue 49, 2023

# Brainteasers – Issue 49, 2023

## Color me confused!

Spencer picks one of the colored numbers from the list below.  He tells the VALUE (only) to Kelly, and the COLOR (only) to Dylan.

After looking at the list (and with no other information provided) Kelly and Dylan have the following conversation:

Kelly:  “I don’t know which one of the colored numbers was picked.”

Dylan: “I don’t either, but I also knew that you didn’t know.”

Kelly: “OK, NOW I know which it is!”

Dylan: “So do I.”

Which of the colored numbers did Spencer originally pick?

[found on Reddit.com – credit to “dingusiesonreddit” – who reports adapting it from a version seen on a Chinese version of a Korean TV game show “Great Escape”]

## Heyawake 1

Heyawake is a logic puzzle with simple rules and challenging solutions.

Color selected cells grid black according to these rules:

• Bold bounded regions with a number should contain that number of black cells.
• Two black cells cannot be directly adjacent horizontally or vertically.
• A column or row of connected white cells cannot span across more than two regions.
• All white cells must be connected (orthogonally) in a single group.

Play an online interactive version of this puzzle here:

https://www.puzzle-heyawake.com/?e=MTozLDUzNCw5MTI=

## Heyawake 2

Play an online interactive version of this puzzle here:

https://www.puzzle-heyawake.com/?e=MToxMiw3ODEsNDM3

Answers

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## Color me confused!  Solution

Spencer chose the White 5

• Kelly’s first comment tells us (and Dylan) that the value appears more than once. So, the value must be 1, 4, 5 or 11.
• Dylan’s first (2-part) comment tells us (and Kelly) that there are no unique values for the color Spenser chose. So, the answer must be either a white or red number (the only two colors which have no unique values).
• When Kelly then asserts knowledge of the answer, it tells us (and Dylan) that it can’t be 1 (if it were 1 – it could be white or red, and Kelly wouldn’t know which). Because Kelly now knows the answer, then we know it must be either the white 5, the red 4 or the red 11.
• When Dylan is also able to solve it, we then know the answer must be the white 5. Because, if it had been a red number, Dylan would still be missing the information to pinpoint whether it was 4 or 11.