The Odd Arithmetic Puzzle

The Odd Arithmetic Puzzle

Create May 27, 2012 / By Barry R. Clarke
The Odd Arithmetic Puzzle

This odd arithmetic, demands a cunning trick!

Carl Friedrich Gauss (1777-1855) was an outstanding German mathematician and is often cited alongside Archimedes and Newton as one the three greatest of all time. By the age of three he was correcting errors in his father's financial calculations and by the age of fifteen he had rediscovered several important mathematical theorems. A year after Gauss's death, Wolfgang Sartorius, Baron von Waltershausen, who worked at the same University as Gauss, published a memorial volume in which he gives an incident that seems to have occurred at school shortly after Carl Friedrich's ninth birthday. It was one that Gauss often liked to relate in old age.

In this [Büttner's] class [of 100 students] the pupil who first finished his example in arithmetic was to place his slate in the middle of a large table. On top of this the second placed his slate and so on. The young Gauss had just entered the class when Büttner gave out for a problem. The problem was barely stated before Gauss threw his slate on the table with the words (in the low Braunschweig dialect): "There it lies." While the other pupils continued, Büttner, with conscious dignity, walked back and forth, occasionally throwing an ironical, pitying glance toward this the youngest of the pupils. The boy sat quietly with his task ended, as fully aware as he always was on finishing a task that the problem had been correctly solved and that there could be no other result. At the end of the hour the slates were turned bottom up. That of the young Gauss with one solitary figure lay on top. When Büttner read out the answer, to the surprise of all present that of young Gauss was found to be correct, whereas many of the others were wrong.

It is often claimed that the problem involved the summation of the numbers 1 to 100, and that Gauss noticed that the sum could be recast as a multiplication where there were 50 pairs that each totalled 101: 1+100, 2+99, 3+98, ..., 50+51. This gives the answer 50x101=5050. However, in "Gauss's Day of Reckoning", an article that appeared in the May-June 2006 edition of American Scientist, Brian Hayes shows that the details of the calculation do not appear in Sartorius's account but were provided much later by Helen Worthington Gauss, the mathematician's great granddaughter, so any claim about the nature of the calculation could be apocryphal. Nevertheless, it is clear that Gauss was far ahead of his peers.

Shakuntala Devi is an Indian calculating prodigy who also demonstrated exceptional mental skills at an early age, performing arithmetic and memory feats at various Universities before the age of nine. In June 1980, she correctly multiplied two 13-digit numbers in 28 seconds, a feat that was recorded in the 1995 Guinness Book of Records.

Although both minds were armed with a toolbox of calculating tricks, a different kind of thinking is required for the following arithmetic puzzle.

Can you rearrange two of the straight lines in the following equation to produce a correct line of arithmetic?


Last Week's Solution

The alien can be found inside a ROCKET. A rotation of the picture a quarter turn counter clockwise shows that the alien is constructed from the letters ROCK. Also, the puzzle asked what the "extraterrestrial" or ET would be in, and the letters ET are also in the word ROCKET.



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