A box can be used for this event instead of a chair. If a chair is used, it is well to have a very sturdy one. This race starts with the players in the same position as in the preceding race, the player on the right hand end of the line sitting... Read more of Chair Sitting Race at Games Kids Play.caInformational Site Network Informational
Privacy
Home Top Rated Puzzles Most Viewed Puzzles All Puzzle Questions Random Puzzle Question Search


The Eight Clowns

(MISCELLANEOUS PUZZLES)



This illustration represents a troupe of clowns I once saw on the Continent. Each clown bore one of the numbers 1 to 9 on his body. After going through the usual tumbling, juggling, and other antics, they generally concluded with a few curious little numerical tricks, one of which was the rapid formation of a number of magic squares. It occurred to me that if clown No. 1 failed to appear (as happens in the illustration), this last item of their performance might not be so easy. The reader is asked to discover how these eight clowns may arrange themselves in the form of a square (one place being vacant), so that every one of the three columns, three rows, and each of the two diagonals shall add up the same. The vacant place may be at any part of the square, but it is No. 1 that must be absent.







Answer:


This is a little novelty in magic squares. These squares may be formed with numbers that are in arithmetical progression, or that are not in such progression. If a square be formed of the former class, one place may be left vacant, but only under particular conditions. In the case of our puzzle there would be no difficulty in making the magic square with 9 missing; but with 1 missing (that is, using 2, 3, 4, 5, 6, 7, 8, and 9) it is not possible. But a glance at the original illustration will show that the numbers we have to deal with are not actually those just mentioned. The clown that has a 9 on his body is portrayed just at the moment when two balls which he is juggling are in mid-air. The positions of these balls clearly convert his figure into the recurring decimal .̍9. Now, since the recurring decimal .̍9 is equal to 9/9, and therefore to 1, it is evident that, although the clown who bears the figure 1 is absent, the man who bears the figure 9 by this simple artifice has for the occasion given his figure the value of the number 1. The troupe can consequently be grouped in the following manner:—









































7 5
2 4 6
3 8 .̍9




Every column, every row, and each of the two diagonals now add up to 12. This is the correct solution to the puzzle.















Random Questions

The Tethered Goat.
Patchwork Puzzles
The Millionaire's Perplexity.
Money Puzzles
The Voters' Puzzle.
Unicursal and Route Problems
Under The Mistletoe Bough
THE SQUIRE'S CHRISTMAS PUZZLE PARTY
The Friar's Puzzle
CANTERBURY PUZZLES
Average Speed.
Money Puzzles
Papa's Puzzle.
Patchwork Puzzles
The Cross Of Cards.
Problems Concerning Games.
An Easy Square Puzzle.
Various Dissection Puzzles
Two Crosses From One
GREEK CROSS PUZZLES
"strand" Patience.
Problems Concerning Games.
The Magic Knight's Tour.
Magic Squares Problem.
The Gentle Art Of Stamp-licking.
Chessboard Problems
The Three Clocks.
Money Puzzles
The Miners' Holiday.
Money Puzzles