Tag Archives: Owen O’Shea

Spot in a Rectangle  Problem

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This puzzle is from the Irishman Owen O’Shea.

“The following puzzle illustrates a beautiful mathematical relationship involving a rectangle of any size and a random point within that rectangle that most people, including mathematicians, are unaware of.

The figure shows a rectangular room.  There is a matchbox located 6 feet from one corner of the room and 27 feet from the opposite corner.  The matchbox is also located 21 feet from a third corner.

How far is the matchbox from the fourth corner?”

Answer.

See the Spot in a Rectangle Problem for a solution.

Weight of Potatoes

The following is another puzzle from the Irishman Owen O’Shea.

“Suppose you buy 100 pounds of potatoes and you are told that 99 percent of the potatoes consist of water.

You bring the potatoes home and leave them outside to dehydrate until the amount of water in the potates is 98 percent.  What is the weight of the potatoes now?”

This problem takes a little concentration to get right and the solution is a bit surprising at first.

Answer

See Weight of Potatoes for solutions.

Distance to Flag Problem

The following puzzle is from the Irishman Owen O’Shea.

“The figure shows the location of three flags [at A, B, and C] in one of the fields on a neighbor’s farm.  The angle ABC is a right angle.  Flag A is 40 yards from Flag B.  Flag B is 120 yards from flag C.  Thus, if one was to walk from A to B and then on to C, one would walk a total of 160 yards.

Now there is a point, marked by flag D, [directly] to the left of flag A.  Curiously, if one were to walk from flag A to flag D and then diagonally across to flag C, one would walk a total distance of 160 yards.

The question for our puzzlers is this: how far is it from flag D to flag A?”

This problem has a simple solution.  But it also suggests a more advanced alternative approach.

Answer.

See the Distance to Flag Problem for a solution.