Thirty-Three Pearls

"A man I know," said Teddy Nicholson at a certain family party, "possesses a string of thirty-three pearls. 
The middle pearl is the largest and best of all, and the others are so selected and arranged that, starting from one end, each successive pearl is worth £100 more than the preceding one, right up to the big pearl. 
From the other end the pearls increase in value by £150 up to the large pearl. 
The whole string is worth £65,000. What is the value of that large pearl?"

"Pearls and other articles of clothing," said Uncle Walter, when the price of the precious gem had been discovered, "remind me of Adam and Eve. 
Authorities, you may not know, differ as to the number of apples that were eaten by Adam and Eve.
It is the opinion of some that Eve 8 (ate) and Adam 2 (too), a total of 10 only. 
But certain mathematicians have figured it out differently, and hold that Eve 8 and Adam a total of 16. 
Yet the most recent investigators think the above figures entirely wrong, for if Eve 8 and Adam 8 2, the total must be 90."

"Well," said Harry, "it seems to me that if there were giants in those days, probably Eve 8 1 and Adam 8 2, which would give a total of 163."

"I am not at all satisfied," said Maud. "It seems to me that if Eve 8 1 and Adam 8 1 2, they together consumed 893."

"I am sure you are all wrong," insisted Mr. Wilson, "for I consider that Eve 8 1 4 Adam, and Adam 8 1 2 4 Eve, so we get a total of 8,938."

"But, look here," broke in Herbert. "If Eve 8 1 4 Adam and Adam 8 1 2 4 2 oblige Eve, surely the total must have been 82,056!"

At this point Uncle Walter suggested that they might let the matter rest. 
He declared it to be clearly what mathematicians call an indeterminate problem.

See answer

Math Genius