This is another imaginative puzzle from MEI’s MathsMonday. I didn’t know what topple blocks were at first, but a previous MathsMonday puzzle defined them as shown in the first frame. Apparently they derive from the game of Jenga created by Leslie Scott and launched in 1983.
See the Topple Blocks Puzzle
This puzzle from Alex Bellos follows the themes in his new book, The Language Lover’s Puzzle Book, which, among other things, looks at number systems in different languages. (See also his Numberphile video.)
“Today is the International Day of the World’s Indigenous People, which aims to raise awareness of issues concerning indigenous communities. Such as, for example, the survival of their languages. According to the Endangered Languages Project, more than 40 per cent of the world’s 7,000 languages are at risk of extinction.
Among the fantastic diversity of the world’s languages is a diversity in counting systems. The following puzzle concerns the number words of Ngkolmpu, a language spoken by about 100 people in New Guinea. (They live in the border area between the Indonesian province of Papua and the country of Papua New Guinea.)
Ngkolmpu-zzle
Here is a list of the first ten cube numbers (i.e. 13, 23, 33, …, 103):
1, 8, 27, 64, 125, 216, 343, 512, 729, 1000.
Below are the same ten numbers when expressed in Ngkolmpu, but listed in random order. Can you match the correct number to the correct expressions?
eser tarumpao yuow ptae eser traowo eser
eser traowo yuow
naempr
naempr ptae eser traowo eser
naempr tarumpao yuow ptae yuow traowo naempr
naempr traowo yempoka
tarumpao
yempoka tarumpao yempoka ptae naempr traowo yempoka
yuow ptae yempoka traowo tampui
yuow tarumpao yempoka ptae naempr traowo yuow
Here’s a hint: this is an arithmetical puzzle as well as a linguistic one. Ngkolmpu does not have a base ten system like English does. In other words, it doesn’t count in tens, hundreds and thousands. Beyond its different base, however, it behaves very regularly.
This puzzle originally appeared in the 2021 UK Linguistics Olympiad, a national competition for schoolchildren that aims to encourage an interest in languages. It was written by Simi Hellsten, a two-time gold medallist at the International Olympiad of Linguistics, who is currently reading maths at Oxford University.”
Here is a challenging problem from the Polish Mathematical Olympiads published in 1960.
“22. Prove that the polynomial
x44 + x33 + x22 + x11 + 1
is divisible by the polynomial
x4 + x3 + x2 + x + 1.”
See the Polynomial Division Problem
(Update 8/23/2021) The idea expressed in this post that mathematicians are “lazy” and seek short-cuts to solving questions and problems, as I did in this one, was recently the subject of a Numberphile post by Marcus du Sautoy: “Mathematics is all about SHORTCUTS“.
Here is another Brainteaser from the Quantum magazine.
“Mr. R. A. Scall, president of the Pyramid Bank, lives in a suburb rather far from his office. Every weekday a car from the bank comes to his house, always at the same time, so that he arrives at work precisely when the bank opens. One morning his driver called very early to tell him he would probably be late because of mechanical problems. So Mr. Scall left home one hour early and started walking to his office. The driver managed to fix the car quickly, however, and left the garage on time. He met the banker on the road and brought him to the bank. They arrived 20 minutes earlier than usual. How much time did Mr. Scall walk? (The car’s speed is constant, and the time needed to turn around is zero.) (I. Sharygin)”
I struggled with some of the ambiguities in the problem and made my own assumptions. But it turned out there was a reason they were ambiguous.
See the Walking Banker Problem for solutions.
