Mathematical Call My Bluff
It has long been a tradition that every year, just before we all break up for Christmas, the TMS hosts a special mathematical adaptation of the cult BBC television quiz show, Call My Bluff.
For those unfamiliar with the procedure, here's roughly how it works. There are two teams of three, together with a host to keep things in order. The teams take it in turns to present three alternative definitions of an obscure mathematical word, only one of which is true—this is done by means of a dazzling, virtuose display of wit and intellect, and occasionally completely unconvincing mathematics. The other team then has the task of deciding which one of the three alternatives is the correct one. If they guess correctly, they get a point; otherwise, their opponents get a point.
2006
The teams this year were:
Team A: Francis Woodhouse, Chris Elliott, Danny McMillan
Team B: Richard Fenn, Tim Dey, Chris Donnelly
and the host was Nathan Kettle. Team A stormed to a convincing victory of 5 points to 1.
Below are the six words selected by the teams, along with the definitions given.
Team A
Word 1: LAZY CATERER
(a) The lazy caterer's sequence is the sequence of numbers given by p = (n2+n+2)/2 and gives the maximum number of pieces of a circular cake, p, which can be created by n straight line cuts.
(b) The lazy caterer problem asks for the minimum number of steps for measuring one litre of water using two containers containing x litres and y litres.
(c) The lazy caterer algorithm gives the minimum length of path for a caterer to clear a set of tables by visiting each table only once and never crossing her path.
Word 2: MOUTH
(a) A principal vertex xi of a simple polygon P is called a mouth if the diagonal [xi-1,xi+1] is an extremal diagonal (i.e., the interior of [xi-1,xi+1] lies in the exterior of P).
(b) A function f from Rn to R has a mouth at x (in Rn) if, for any d1, d2 < R (some real R), we have f(x - r1) < f(x - r2) for all r1, r2 in Rn satisfying |r1 - x| = d1, |r2 - x| = d2.
(c) An oscillatory system where the level of damping is far greater for one sign of the velocity than the other (i.e. level of damping is dependent on sign(x').)
Word 3: GIFT WRAP THEOREM
(a) No subspace of Rn is homeomorphic to the n-sphere.
(b) For n>2 we can form exactly n+2 n-dimensional regular polytopes (i.e polytopes that can be 'unfolded' to regular polytopes of dimension n-1).
(c) For any paper folded by a number of simple flat folds (straight folds that can be folded flat on a surface), the resulting fold pattern can be 2-coloured.
(The correct answers are (a) in each case.)
Team B
Word 1: FLYPE
(a) To fold or turn back (a move in knot theory). The root is an auld Scots word.
(b) The probability function of an electron moving in a 3d random walk (like a fly) - the probability of it going in a specific direction (e.g. towards an attractor) is a function of the charge - hence, 'fly - pe'.
(c) An adjective stating that it's a polynomial (on [0,1]) with all coefficients 0 except those x with order 23^n. It is a probability distribution which is used to estimate the odds of milk going off before a certain time.
Word 2: TUPPER'S FORMULA
(a) A formula which when graphed looks like the symbols in the formula itself.
(b) The formula used to verify the check digit on a bar-code.
(c) A formula which generates sexy primes, that is primes such that p and p+6 are both prime.
Word 3: ZEISEL NUMBER
(a) http://mathworld.wolfram.com/ZeiselNumber.html
(b) http://mathworld.wolfram.com/AlmostInteger.html
(c) http://mathworld.wolfram.com/TangentNumber.html
(The correct answers are (a) in each case.)
2005
The teams this year were:
Team A: Nathan Kettle, Andy Davies, Matt Lee
Team B: Ed Hill, Sam Kemp, Jon De Souza
together with your host, Paul Smith. Team B won by 5 points to 1.
Below are all six words, together with all eighteen definitions.
Team A
Word 1: NARCISSISTIC
(a) A triangle where the area of the largest inscribed square on each side of the triangle is the same for each side, strangely there is only one such triangle apart from the equilateral triangle.
(b) An n digit number which equals the sum of the nth powers of its digits, e.g. 153.
(c) An image such that for every point in the image there exists a line of symmetry of the image passing through that point, e.g. a circle or any collection of parallel lines.
Word 2: EVIL
(a) An evil number is a number where the first n digits after the decimal point of the number add up to 666.
(b) An evil knot is a knot that requires further crossings to be made before it becomes unknotted.
(c) The evil function is that of the sum of n from 1 to infinity of [nx]/(2^n) for 0Mathworld).
"Word" 3: RPN
(a) Ramanujan prime number - A primorial (like a factorial) of a prime p is the product of all the primes less than or equal to p. The famous Trinity mathematician Srinivasa Ramanujan conjectured the RPN conjecture that there are infinitely many primes which are one more than a primorial number. Ramanujan himself calculated the first 6 such primes, the largest of which was 9,699,691.
(b) Reverse Polish Notation - Reverse Polish notation (RPN) is a method for representing expressions in which the operator symbol is placed after the arguments being operated on. Polish notation, in which the operator comes before the operands, was invented in the 1920s by the Polish mathematician Jan Lucasiewicz. Later it was suggested placing the operator after the operands and hence created reverse polish notation. For example, the RPN expression 2 3 + will produce the sum of 2 and 3.
(c) Rwandan Pigmy Numerals - The earliest known inhabitants of what is now Rwanda were the Twa Pygmies, an ethnic group that still lives in the country today but makes up only a paltry 1% of the population. When German colonisers arrived in the 1900's they discovered that the pigmies were using a number system which roughly approximated base 5. Although the number system has been completely lost from the major cities, some traditional pigmy villages do still write prices first in RPN and then in base 10 which they are now required to do so under Rwandan Law.
(The correct answers are (b), (a), (b).)
Team B:
Word 1: STRATARITHMETRY
(a) The art of drawing up an army or body of men in a given geometrical figure, and of estimating the number of men contained in such a figure. (stratos = army.)
(b) A corruption of straturarithmetic - stratura = pavement - calculations to do with tessalations att. Conway.
(c) stratum = streaching - The use of or involving the group of loops in a contractible space.
Word 2: ANALEMMA
(a) An orthographic projection of the sphere onto a plane - from L.= sundial.
(b) bipartition of a set based on a single property - from Fr. an (into) + alembus (distilling apparatus).
(c) The external surface of a geometrical figure - from Gk. ana (up) + lemma (shell).
Word 3: NIALPDROME
(a) A number whose hexadecimal digits are in nonincreasing order. The first few are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 32, 33, 34, 48, 49, 50, ...
(b) A number who digits can be rearranged to form a palindrome.
(c) In large sample theory, a data set for which there exists a sufficiently high probability that the data are from a normal distribution.
(The correct answers are all (a).)
2004
This year's game was held on Monday, 29 November. The teams were:
Team A: James Cranch, Gavin Johnstone, Richard Gibson
Team B: Chris Cummins, Victor Falgas, Paul Smith
with Vicky Neale as your host. Team A won by the convincing margin of 5 points to 1. Below you'll find the six words used by the teams together with their correct definitions.
Team A:
Word 1: RAMPHOIDAL: Relating to a cusp of higher order, where both branches lie on the same side of the tangent to the cusp.
Word 2: KIRKMAN'S SCHOOLGIRL PROBLEM: In a boarding school there are fifteen schoolgirls who always take their daily walks in rows of threes. How can it be arranged so that each schoolgirl walks in the same row as each other schoolgirl exactly once a week? (The solution of this problem is equivalent to constructing a Kirkman triple system of order 2.
Word 3: OPHIURIDE: In about 180BC, a charming contemporary of Apollonius, by the name of Diocles, was engaged in one of his many unproductive attempts to double the cube. Whilst doing so, he invented a cubic, described in his famous text, On Burning Mirrors, that came to be known as the Cissoid of Damocles. The ophiuride is simply a cubic curve which generalizes this, and can be given by the equation x(x2 + y2) + (ax - by)y = 0.
Team B:
Word 1: BEVAPRIME: A prime number with a billion digits.
Word 2: PULVERIZER: A seventh century name for the method of solving the Diophantine equation ax + by = c using Euclid's algorithm.
Word 3: CHASLES' RELATION: A fundamental theorem of geometry which says that for three points A, B, C on a line, the sum of the line segments AB + BC + CA is zero.
If anyone would like to see the alternative definitions used by the teams, please nag either the webmaster or the Secretary.
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