Estimation quiz!

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A different approach to estimation with respect to spherical density packing from the August 1974 (v1 n2) edition of HP-65 Key Notes …

"HP-65 + 4 ,757 = SX-70

   The above photo was taken with a new Polaroid SX-70 camera won at Las Vegas-and therein lies a really fantastic "believe-it-or-not" story for all you HP-65 fans.
   The man in the photo is Emmett Ingram, Jr., Chief Engineer at Jetronix Radio Engineering Labs in Palos Verdes, California. And if you find it difficult to believe his story, then you just don't know Emmett. (I do; I've met him. An incredible man. And the story is true. Ed.)
   If you happened to attend the NEWCOM show in Las Vegas in May, 1974, you probably remember that the United Technical Publications booth had a large plastic tank containing many marbles and the three volume set of the Electronic Engineers Master (EEM). There was a prize for guessing the correct (or nearest to, correct) number of marbles in the rectangular tank, and the prize was (you've guessed it!) a brand new Polaroid SX-70 camera. Well, Emmett decided he wanted to win that camera and, besides, the problem was a real challenge for his trusty HP-65, which he is NEVER without.
   First, Emmett measured the container, two-thirds full of marbles, subtracting the volume occupied by the three-volume set of the Electronic Engineers Master. Then he counted and recounted those exposed marbles per row on each of the four sides of the tank. He also counted each marble tangent to the plastic face of the container. Of those marbles that appeared to touch the face of the plastic tank, a count determined that 42.7% actually did. Armed with those numbers, he went to the local Las Vegas ten-cent store and purchased all the marbles they had in stock ($5.80 worth). Then off to the photo store next door, where he picked up a 1,000 cc graduated beaker. Then he cut off the top of a 6-quart bottle that he had found in the alley, added water, measured, counted, and computed.
   Following all of this, Emmett placed a long-distance telephone call to a U.S.C. mathematician. (You can imagine the conversation!) He advised Emmett that the data gathered would best fit the Chi Squared Probability equation. All of this was then pumped into Emmett's trusty HP-65, and out popped 4,757.
   The correct number of marbles in the container was 4,754, which represented the total number of pages in the '74 edition of Off The-Shelf (O-T-S) and the '73-'74 edition of EEM. Naturally, the people at United Technical Publications were astonished by Emmett's wild but accurate guess, and even more astonished when he told them it was not a guess, it was a carefully calculated answer!
   As a matter of record, if the quality control on the marbles that Emmett bought had been better, it's probable that he would have hit 4,754 right on the nose! According to Emmett: "Some marbles measured to be nonspherical by 0.05% (4754/4757, an error of 0.063%). It appears a few of the marbles escaped the manufacturer's quality control and fouled me up by a count of three!"
   So, that's the story. We're grateful to Emmett for allowing us to share it with all you other HP-65 owners. We're also grateful to Emmett for his staunch support of HP calculators, He's owned an HP-35, HP-45, HP-80, and now the HP-65."

BEST!
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