#72 A long lane
The mathematician Professor Numero lives at number 13 Long Lane, the same road as his good friend Professor Lemma, who is at number 156. The friends like that their house numbers when multiplied together are exactly divisible by the two numbers added together. However, Numero has always had his eye on number 28, which he thinks is 鈥減erfect鈥�. 鈥淚f only Lemma could also move so that our houses still had the same mathematical relationship,鈥� says Numero. Bearing in mind that Long Lane lives up to its name, what is the biggest house number that Lemma could move to?
Answer next week
#71 White lines
Solution
It requires a minimum of four lines to link all white squares. The two white corners (A and B) must be start/end points because they touch only one other white square. Start at A and your first move is to C. The edge square D will be stranded unless the line from C goes into D. The same logic follows around all edge squares which gets you to B. This covers 14 white squares and effectively reduces the problem to a new one with a 6脳6 chess board. The same procedure with a new line reduces the board to 4脳4. A third line gives a 2脳2 board. The final two squares are then covered by a fourth line.
Quick quiz #64
1 The structure of which substance allegedly came to chemist August Kekul茅 during a dream of a snake biting its tail?
2 What might you measure using a Wheatstone bridge?
3 What form of pneumonia, usually caused by contaminated water, was first identified in an outbreak at a Philadelphia hotel in 1976?
4 What geological era, noted for an explosion in invertebrate life and named after a Welsh Celtic tribe, was sandwiched between the Cambrian and Silurian eras?
5 Io, Europa, Ganymede鈥� what鈥檚 missing?
Answers on page 54
Answers
1 Benzene. With the chemical formula C6H6, this constituent of crude oil has a central ring of six carbon atoms
2 Electrical resistance
3 Legionnaires鈥� disease, so called because the outbreak occurred at a convention of the American Legion
4 The Ordovician, which ran from 485.4 to 443.8 million years ago
5 Callisto, to complete the list of the four 鈥淕alilean鈥� moons of Jupiter first observed in 1610