Timing the Car

This is yet another simple problem from Henry Dudeney.

“57. TIMING THE CAR

“I was walking along the road at three and a half miles an hour,” said Mr. Pipkins, “when the car dashed past me and only missed me by a few inches.”

“Do you know at what speed it was going?” asked his friend.

“Well, from the moment it passed me to its disappearance round a corner I took twenty-seven steps and walking on reached that corner with one hundred and thirty-five steps more.”

“Then, assuming that you walked, and the car ran, each at a uniform rate, we can easily work out the speed.” ”

Answer.

See Timing the Car for a solution.

Post Views: 124

Amazing Root Problem

Well, I discovered that the 2024 Math Calendar has some interesting problems, so I guess things will limp along for a while.  This is a challenging but imaginative problem from the calendar.

_______________

As before, recall that all the answers are integer days of the month.

Answer

See the Amazing Root Problem for a solution.

Post Views: 115

Five Year Anniversary

So I managed to make it five years.  Again, I thought I would present the statistical pattern of interaction with the website in the absence of any explicit feedback.

But as the summary shows, the fall-off of visitors that began in the middle of last year has persisted throughout 2023.  I have also run out of much new material, so I am basically going to wrap it up.  I have a few things in the hopper, but they are mostly similar to puzzles already presented.  I have one or two essay ideas left, but again I have mostly said what I have to say, and the world of math has moved on.

Anyway, here is the summary for what it’s worth.

See Five Year Anniversary

Post Views: 258

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.

Post Views: 148

More Right Triangle Magic

James Tanton asked to prove the following surprising property of a right triangle and its circumscribed and inscribed circles.

“Every triangle is circumscribed by some circle of diameter D, say, and circumscribes another circle of smaller diameter d. For a right triangle, d + D equals the sum of two side lengths of the triangle. Why?”

See More Right Triangle Magic

Post Views: 178

Two Containers Mixing Puzzle

This is a slightly different type of a mixture problem from Dan Griller.

“Two containers A and B sit on a table, partially filled with water.  First, 40% of the water in A is poured into B, which completely fills it.  Then 75% of the water in B is poured into A, which completely fills it.  80% of the water in A is poured into B, which completely fills it.  Calculate the ratio of the capacity of container A to the capacity of container B, and the fraction of container A that was occupied by water at the start.”

Answer.

See the Two Containers Mixing Puzzle for solution.

Post Views: 343
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