This is another typical travel puzzle from the 2024 Math Calendar.
“A boat travels downriver at 30 mph, then goes back up along the same path at 20 mph. What is the boat’s average speed?”
As before, recall that all the answers are integer days of the month.
See Another Boat Puzzle for a solution.
This is a simple 1917 puzzle from Henry Dudeney.
“During a visit to the seaside Tommy and Evangeline insisted on having a donkey race over the mile course on the sands. Mr. Dobson and some of his friends whom he had met on the beach acted as judges, but, as the donkeys were familiar acquaintances and declined to part company the whole way, a dead heat was unavoidable. However, the judges, being stationed at different points on the course, which was marked off in quarter-miles, noted the following results:—The first three-quarters were run in six and three-quarter minutes, the first half-mile took the same time as the second half, and the third quarter was run in exactly the same time as the last quarter. From these results Mr. Dobson amused himself in discovering just how long it took those two donkeys to run the whole mile. Can you give the answer?
See Donkey Riding for solutions.
This is a problem from the 629 AD work of Bhaskara I, a contemporary of Brahmagupta.
“A fish is resting at the northeast corner of a rectangular pool. A heron standing at the northwest corner spies the fish. When the fish sees the heron looking at him he quickly swims towards the south (in a southwesterly direction rather than due south). When he reaches the south side of the pool, he has the unwelcome surprise of meeting the heron who has calmly walked due south along the side and turned at the southwest corner of the pool and proceeded due east, to arrive simultaneously with the fish on the south side. Given that the pool measures 12 units by 6 units, and that the heron walks as quickly as the fish swims, find the distance the fish swam.”
See Lunchtime at the Fish Pond for a solution.
This is a problem from the 2000 Olymon (the Mathematics Olympiads Correspondence Program) for secondary students sponsored jointly by the Canadian Mathematical Society and the Mathematics Department of the University of Toronto.
Find the value of S.”
See Astronomical Sum for solutions.
This is a puzzle from Talwalkar’s set of “Impossible Puzzles with Surprising Solutions.”
“Call this puzzle the leaning tower of rhombi.
There are 5 isosceles triangles, aligned along their bases, with base lengths of 12, 13, 14, 15, 16 cm. The 10 quadrilaterals above are in rows of 4, 3, 2, and 1. Each quadrilateral is a rhombus, and the top of the tower is a square. What is the area of the square?”
See Stacked Rhombuses Puzzle for solutions.
This is a slightly stimulating thought puzzle from Futility Closet.
“You have three identical bricks and a ruler. How can you determine the length of a brick’s interior diagonal without any calculation?”
See A Simple Plan
This is a fairly straight-forward problem from A+ Click.
“The water from an open swimming pool evaporates at a rate of 5 gallons per hour in the shade and 15 gallons per hour in the sun. If the pool loses 8,400 gallons in June and there were no clouds, what is the average duration of night during that month?”
Answer Choices: 6 hours 8 hours 10 hours 12 hours
See Evaporating Pool Problem for solutions.
This is a curious relation from the 2024 Math Calendar.
“10! seconds is exactly how many weeks?”
As before, recall that all the answers are integer days of the month, and also recall that 10! = 10x9x8x … x3x2x1.
See a Curious Calendar Puzzle for a solution.
This is an old puzzle from Catriona Agg that I found on BL’s Math Games website.
“All four triangles are equilateral. What fraction of the largest triangle is shaded?”
This problem turned out to be both easy and unexpectedly challenging, at least for me.
See Four Equilateral Triangles for solutions.
I see another icon of the past has passed away: Tom Lehrer. Lehrer was a mathematician who put his talents to great use, in contrast with mathematicians like the neocon Paul Wolfowitz and Iraqi Ahmed Chalabi who helped foment the Iraq War. He skewered all the shibboleths of the times (1950s and 60s) with his pre-politically-correct take-downs, mainly to the music of Gilbert and Sullivan.
Among his targets was the “New Math”—the Common Core of 60 years ago and a reminder that some things never change. Fortunately, the New Math infiltrated public schools after my time, but you will recognize that its purpose is for students to understand math and not just perform rote manipulations. A truly noble intent, but its continued reincarnation indicates how difficult it is to achieve. So we are left with humor at our folly.
This video of “New Math” is from a live 1965 performance of “That Was the Year That Was”. A more famous song is Lehrer’s musical rendition of the chemical periodic table, “The Elements” (performed live in 1967 in Denmark). I invite you to listen to all his songs for an irreverent window into the past.
See “Tom Lehrer Dies at 97” for a PDF copy of his obituary.
