A Wordsearch with Only One Word

Logic Level 4

The above is an 8x8 wordesearch, in which only 6 letters are visible. Your goal is the find the word "BEE".

  • You know that BEE can appear in any "compass" direction. That is, it can appear left-to-right, backwards, diagonally in any orientation, etc.

  • You know that BEE appears exactly once .

  • You know that "B" and "E" are the only two letters filling the grid.

Where is the word "BEE"?

Answer Extraction: Impose a coordinate system where ( i , j ) (i,j) is the square in the i i th column from the left and the j j th row from the bottom, so that the bottom-left square is (1,1). If the "B" of the BEE is located at the square with coordinates ( x , y ) (x,y) , then input x ⋅ y x \cdot y


The answer is 15.

Bryan Hung by Bryan Hung , 20, USA

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3 solutions

Jon Haussmann
May 5, 2019

The diagram below shows a possible grid. I don't know if it is unique.

4 Helpful 3 Interesting 2 Brilliant 1 Confused

It is pretty easy to show that the starting letter of the word BEE must occur in the 5th or 6th columns. More detailed checking makes the 6th column impossible, and it is relatively easy to show that, with the initial B of BEE in the 5th column, it has to occur in the 3rd row.

Yes, the placement of BEE is unique, but, as Bryan says, the grid is not.

Mark Hennings - 2 years, 1 month ago

The grid is not unique, but the location of BEE is.

Bryan Hung - 2 years ago

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Second grid then, please.

Mark Hennings - 2 years ago

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Just turn an isolated B into an E.

Bryan Hung - 2 years ago

Check out my solution for your query!

Charlz Charlizard - 1 year, 5 months ago
Charlz Charlizard
Dec 26, 2019

Here I found the another solution. The E's in my 1st solution is the maximum number of E's we can get. So this question can be improved by asking the maximum number of B's or E's in the solution. That would have just one solution.

The base logic is same: first you start out by filling all diagonals from the given E's until they are cornered. Then start filling out all B's. Then see which spot is not attached with the string of E's so when changed doesn't have any affect on the remaining placements.

1 Helpful 0 Interesting 0 Brilliant 1 Confused

While it does get the right answer, the actual proof that the location of BEE is unique requires a lot more work than it might seem!

Bryan Hung - 1 year, 5 months ago

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Yeah, it is hard to generalize but an algorithm can be devised!

Charlz Charlizard - 1 year, 5 months ago
Saya Suka
May 3, 2019

All shown Es have the same parity but the southern one. Only then I can see that the layout was alternate placing of Bs and Es except that uglEE duckling. That simple, single change won't cause any issues diagonally since they're all full of Bs and horizontally it'll be BEEEB.

0 Helpful 0 Interesting 0 Brilliant 2 Confused

Several problems here:

  1. Does "BEEEB" not have two "BEE"s?
  2. How do you know that the placement of BEE is unique?

Bryan Hung - 2 years, 1 month ago

By trial and error, this is the only unique solution

Chris Sapiano - 2 years, 1 month ago

The question is SHIT!

Sai Teja Uppili - 1 year, 8 months ago

1 pending report

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