Benjamin Banneker's Riddle

Benjamin Banneker (1731-1806) is regarded as the first African-American inventor.  He was also a gifted mathematician.  Here is a riddle he devised.

Divide 60 into four such parts that the first being increased by 4, the second decreased by 4, the third multiplied by 4, the fourth part divided by 4, that the sum, the difference, the product and the quotient shall be one and the same number.

Rather than try solving this by "guess and check," try to solve it algebraically.  Scroll down for the answers and a link to the mathematical solution.

The first number is 5.6 (5.6+4=9.6)

The second number is 13.6  (13.6-4=9.6)

The fourth number is 2.4  (2.4*4=9.6)

The fifth number is 38.4  (38.4/4=9.6)

And 5.6+13.6+2.4+38.4=60

Here's another puzzle he created:

A cooper and a vintner sat down for a talk,
Both being so groggy that neither could walk;
Says cooper to vintner, "I'm the first of my trade,
There's no kind of vessel but what I have made,
And of any shape, sir, just what you will,
And of any size, sir, from a tun to a gill."
"Then,"says the vintner, "you're the man for me.
Make me a vessel, if we can agree,
The top and the bottom diameter define,
To bear that proportion as fifteen to nine,
Thirty-five inches are just what I crave,
No more and no less in the depth will I have;
Just thirty-nine gallons this vessel must hold,
Then I will reward you with silver or gold --
Give me your promise, my honest old friend."
"I'll make it tomorrow, that you may depend!"
So, the next day, the cooper, his work to discharge,
Soon made the new vessel, but made it too large;
He took out some staves, which made it too small,
And then cursed the vessel, the vintner, and all.
He beat on his breast, "By the powers" he swore
He never would work at his trade any more.
Now, my worthy friend, find out if you can,
The vessel's dimensions, and comfort the man!

Solution: [As noted by Martha Tyson in an unpublished manuscript entitled "A Memoir," and by W.W. Allen...Benjamin Hallowell of Alexandria, Virginia was reported to have proposed as his solution 24.745 inches and 14.8476 inches for the diameters. Banneker had not provided a solution to the problem.]

If you want more Banneker puzzles, visit here

Presumption should never make us neglect that which appears easy to us, nor despair make us lose courage at the sight of difficulties.

Banneker

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