Rhind papyrus mathematical puzzle

Ancient Egyptians kept records of lunar phases and seasons to be used either for religious or agricultural purposes. Surveyors in ancient Egypt used body parts as unit measurements for lands and buildings. With time however, these units would prove to be cumbersome and thus the need to come up with easier and convenient mathematical models that would be used in solving an array of problems. This is how the Rhind papyrus came about. It is an arithmetic and geometric manual that demonstrates how the Egyptians used multiplication and division in their activities ("Egyptian Papyri", 2016). It also has evidence of other mathematical concepts such as composite numbers, unit fractions, and a demonstration of how to solve linear equations as well as geometric and arithmetic series (ronknott.com, 2016). Multiplication entailed the process of a repeated doubling of the number to be multiplied on one column and the other number on a separate column, which in essence is a multiplication of binary factors. Multiplication of 41 by 59, for instance would proceed as follows:

41 59 ____________ 1 59 2 118 4 236 8 472 16 944 32 1888

As 64 is greater than 41, there is no point of proceeding beyond the 32 entry. 41 is the summation of 32, 8 and 1. The next step is adding the numbers on the right column that correspond to 32, 8 and 1 which yield 2419.

Trade in the market place demanded the use of fractions. The papyri which have been handed down from generations have demonstrated the application of unit fractions which is based on the symbol of the Eye of the Horus where each side of the eye is a representation of a fraction of the whole, each half of the previous one, that is ,1/8..1/64. This was the first known demonstration of a geometric series. If for instance they needed to divide 3 loaves among five people, they would first divide the first two into thirds and the last into fifths. Each of these fifths would later be divided into thirds such that each person would receive 3/5 i.e. 1/3+1/5+1/15. Ancient civilizations were not even aware of the math in the puzzles they were solving, it was a thing that they took for granted ("A popular Chinese game: the Qi Qiao Tu, or Tangram - Asian and African studies blog", 2016).

Dodgson (Carroll) s Tangrams

Tangrams is an entertaining yet complicated puzzle that involves the use of 7 flat shapes combined with a players imagination. All the pieces must touch each other but should not overlap. Its origins can be traced to China where it has deep traditions. Chinese tangram books originally had the silhouettes that were to be constructed using the flat shapes and the solution that is how the different pieces would be arranged to come up with the desired shape. Lewis Carroll, a mathematician, would later develop his book Alice in Wonderland using the seven pieces in tangram. For these different shapes to perfectly fit, mastery of the concept of angles and symmetry is required.

Fibonacci's sequence

Different puzzles employ the concept of Fibonacci series in their execution. If, for instance we want to solve a puzzle that involves building a wall using bricks whose length is twice its height, several different patterns can be used, depending on our desired length of the wall. There is a one wall pattern made by putting the brick to stand on its end; 2 different patterns for a wall made using two bricks: making the bricks stand long-ways adjacent to each other and placing them to lie one on top of the other ("Egyptian Papyri", 2016). To determine the number of patterns that can be obtained for a wall using varying number of bricks, the Fibonacci formula can be employed where f(n)=f(n-1) +f(n-2) where f(n) is the number of patterns for walls of height 2 and length n.

Cardan's Rings

In this puzzle, each of the rings is attached to the post with an exception of the ring furthest from the handle. Initially, all the rings go through the skewer. The game requires that the player should remove the skewer from the rings and then put it back as before. The number of moves to put the rings on and off is essentially the same. These moves can be represented mathematically by the relation M (n) = M (n-1) + 2M (n-2) + 1 where m (n) represents the number of moves

Sam Loyd and his 15 puzzle

The basic form of the puzzle comes in a 4 by 4 grid that is made by sliding counters in a tray. There is a total of 16 counters numbered 1 to 15. The 16th slot is empty. The tiles are randomly shuffled by haphazardly scrambling them to any position. The player is required to solve the puzzle by rearranging the tiles in a consecutive order. An understanding of permutations would be helpful in solving this puzzle.

PASCALS Triangle

This is an arrangement of numbers in a triangular form such that a particular number in the triangle is represented by the sum of two numbers above it. Pascals triangle can be used in the determination of probabilities of obtaining heads or tails when you toss a coin.

References

A popular Chinese game: the Qi Qiao Tu, or Tangram - Asian and African studies blog. (2016). Britishlibrary.typepad.co.uk. Retrieved 8 July 2016, from http://britishlibrary.typepad.co.uk/asian-and-african/2014/11/a-popular-chinese-game-the-qi-qiao-tu-or-tangram.html

Egyptian Papyri. (2016). Www-groups.dcs.st-and.ac.uk. Retrieved 8 July 2016, from http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Egyptian_papyri.html

ronknott.com, D. (2016). How to prove a the Brick Wall series really is the FIBONACCI SERIES. Personal.maths.surrey.ac.uk. Retrieved 8 July 2016, from http://personal.maths.surrey.ac.uk/ext/R.Knott/Fibonacci/brickEXPLAIN.html

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