Prospectors had struck oil on the Lazy D ranch in the Texas panhandle, and Cyrus Q Harbuckle, the owner of the land, was installing pipelines to carry the oil from the wellhead to the boundaries of his property.
The Lazy D was rectangular in shape, and the plan was to run a pipe from the wellhead to each corner of the ranch.
"Whar'bouts is this h'yar well?" asked the pipeline engineer, who was seven feet tall without his Stetson and known as Shorty. "Ah gotta work out how much pipe to buy."
"Don' rightly recall, Shorty" said Cyrus. "But ah know it's ten miles from the north-east corner, two miles from the northwest, and five miles from the southwest."
"How far is it from the southeast corner?"
"Uh. Dang me if ah ain't fergot."
"How big is ya ranch, Cyrus?"
"Ah fergot that, too. It's purty small as they go h'yarabouts. Does it matter?"
"It'd make life a danged sight easier, Cyrus. But maybe it don' matter."
How many miles of pipe should Shorty buy?
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The answer
Shorty needs 28 miles of pipe.
Pythagoras's theorem tells us that:
u2 = a2+c2
v2 = b2+c2
w2 = b2+d2
x2 = a2+d2
So u2+w2 = v2+x2
since both equal a2+b2+c2+d2.
We are told that u = 10, v = 2, w = 5.
Therefore 100+25 = 4+x2, so x2 = 121, so x = 11.
The total length of pipe is 10+2+5+11 = 28.
The winner is Gwynfryn E Pritchard from Cardiff
