perplexus.info :: Logic : A's, B's, C's and D's 2

A's, B's, C's and D's 2 (Posted on 2019-07-03)

Place one of A, B, C or D into each of the 25 empty squares so that the number of letters in each row and column match the number indicated on that row and column for that letter.

Identical letters cannot be next to each other vertically or horizontally, but may be adjacent diagonally.




                 +---+---+---+---+---+
              A  | 2 | 2 | 0 | 1 | 1 |
                 +---+---+---+---+---+
              B  | 1 | 1 | 2 | 2 | 0 |
                 +---+---+---+---+---+
              C  | 2 | 1 | 1 | 0 | 1 |
                 +---+---+---+---+---+
  A   B   C   D  | 0 | 1 | 2 | 2 | 3 |
+---+---+---+---++===+===+===+===+===+
| 0 | 2 | 1 | 2 ||   |   |   |   |   |
+---+---+---+---++---+---+---+---+---+
| 1 | 1 | 2 | 1 ||   |   |   |   |   |
+---+---+---+---++---+---+---+---+---+
| 2 | 0 | 2 | 1 ||   |   |   |   |   |
+---+---+---+---++---+---+---+---+---+
| 2 | 1 | 0 | 2 ||   |   |   |   |   |
+---+---+---+---++---+---+---+---+---+
| 1 | 2 | 0 | 2 ||   |   |   |   |   |
+---+---+---+---++---+---+---+---+---+

From Mensa Puzzle Calendar 2019 by Fraser Simpson, Workman Publishing, New York. Puzzle for June 26.

See The Solution Submitted by Charlie

Rating: 5.0000 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

P&P solution a'la Feynman

Comment 14 of 13

In one of Feynman's books he write about being able to do a lot of computations quickly by knowing just two common logarithms to three decimal places: log2=.301 and log3=.477

12^37 = (2*2*3)^37

Log(12^37)=37*(log2+log2+log3)=37*1.079=39.923

so the number is 10^39.923 = (10^0.923)*(10^39)

Focus on 10^0.923

log8=3log2=3*.301=.903

log9=2log3=2*.477=.954

Since our exponent between these, 10^0.923 is between 8 and 9, hence it begins with 8.

Mr. Feynman practiced this enough that he could do it in his head. I console myself that I did manage it with only P&P

Posted by Jer on 2020-11-18 11:04:21

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