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- Math
Goldbach Computations
In 1742, historian and mathematician Christian Goldbach (1690–1764) wrote a letter to Leonhard Euler (1707–1783) in which he suggested, in effect, that every integer greater than 5 is the sum of three prime numbers. A prime number is evenly divisible only by itself and 1. Nowadays, Goldbach’s conjecture is expressed in the following equivalent form: […]
- Math
A Magic Knight’s Tour
For as long as chessboards have existed, there have been puzzles involving chessboards and chess pieces. Some of the most enduring conundrums involve knights. Example of a knight’s tour in which the rows and columns have the same sum (260), but the diagonals add up to 348 and 168. According to the rules of chess, […]
- Math
The Bias of Random-Number Generators
Some popular random-number generators fail even in simulating a coin toss.
- Math
Rolling with Reuleaux
Have you ever wondered why the cover of a manhole is nearly always round? Why isn’t it oval or square? Reuleaux curve based on an equilateral triangle. Reuleaux curves based on the pentagon (top) and heptagon (bottom). The usual answer is that a circular lid, unlike a square or an oval cover, won’t fall through […]
- Math
Trimathlon Palindromes
“A man, a plan, a canal–Panama.” This statement is a famous example of a palindrome–a phrase that reads the same forward or backward. Inventive wordsmiths and puzzlists have come up with all sorts of words, sentences, and even paragraphs that have this property. The term palindrome can also be applied to whole numbers, such as […]
- Math
Pennant Races and Magic Numbers
It’s getting close to the end of the regular baseball season. Fanatic fans track not only which team is in first place or in position for a wild-card berth in the playoffs but also the number of games a team must win to avoid elimination. The elimination, or “magic,” number is usually defined to be […]
- Math
Hyperbolic Five
Dutch graphic artist M.C. Escher (1898–1972) devised many highly original schemes in his attempts to capture the concept of infinity visually. One strategy he often employed was to create repeating patterns of interlocking figures. However, although he could imagine how such arrays extended to infinity, the actual pattern he drew represented only a fragment of […]
- Math
SET Math
The card game known as SET® is deceptively simple. Its object is to identify, as quickly as possible, a grouping (SET) of three cards, selected from 12 cards laid out face up on a table. A SET deck has 81 (34) cards. Each card displays a design with four attributes: shape, number, shading, and color. […]
- Math
Golf Clubs and Driving Distance
The last 20 years have seen remarkable changes in golf equipment: metal-headed drivers, forgiving irons, new putter variants, juiced golf balls, and more. Have these technology changes led to improved performance? Anecdotal evidence certainly points to such improvements. In 1980, for example, the leader in driving distance on the Professional Golfers of America (PGA) Tour […]
- Math
Running Lanes and Extra Steps
When going out to your local running track for a workout, you sometimes find that you are allowed to use only certain lanes for training. On any looped track, however, the outer lanes are longer than the inner lanes. That presents a problem for someone using the track for speed workouts. A four-lane equal-quadrant running […]
- Math
Perfect Pyramids
The tetrahedron is the simplest of all polyhedra—solids bounded by polygons. It has four triangular faces, four vertices, and six edges. If each edge has the same length and each face is an equilateral triangle, the result is a regular tetrahedron—one of the Platonic solids. Example of a tetrahedron. Another group of tetrahedra that some […]
