Posts Tagged ‘ Le Monde ’

Le Monde puzzle [#739]

September 9, 2011
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Le Monde puzzle [#739]

The weekend puzzle in Le Monde this week is again about a clock.  Now, the clock has one hand and x ticks where a lamp is either on or off. The hand moves from tick to tick and each time the lights go on or off depending on whether or not both  neighbours were in

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Le Monde puzzle [#738]

September 1, 2011
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Le Monde puzzle [#738]

The Friday puzzle in Le Monde this week is about “friendly perfect squares”, namely perfect squares x2>10 and y2>10 with the same number of digits and such that, when drifting all digits of x2 by the same value a (modulo 10), one recovers y2. For instance, 121 is “friend” with 676. Here is my R

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Le Monde puzzle [#737 re-read]

August 27, 2011
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Le Monde puzzle [#737 re-read]

As a coincidence, while I was waiting for the solution to puzzle #737 published this Friday in Le Monde, the delivery (wo)man forgot to include the weekend magazine and I had to buy it this morning with my baguette (as if anyone cares!). The solution is (y0,z0,w0)=(38,40,46) and…it does not work! The value of (x1,y1,z1,w1) is

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Le Monde puzzle [#737]

August 26, 2011
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Le Monde puzzle [#737]

The puzzle in the weekend edition of Le Monde this week can be expressed as follows: Consider four integer sequences (xn), (yn), (zn), and (wn), such that and, if u=(xn,yn,zn,wn), for i=1,…,4, if ui is not the maximum of u and otherwise. Find the first return time n (if any) such that xn=0. Find the value

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Ternary sorting

July 24, 2011
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Ternary sorting

The last Le Monde puzzle made me wonder about the ternary version of the sorting algorithms, which all seem to be binary (compare x and y, then…). The problem is, given (only) a blackbox procedure that returns the relative order of three arbitrary numbers, how many steps are necessary to sort a series of n

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Le Monde puzzle [#14.2]

May 14, 2011
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Le Monde puzzle [#14.2]

I received at last my weekend edition of Le Monde and hence the solution proposed by the authors (Cohen and Busser) to the puzzle #14. They obtain a strategy that only requires at most 19 steps. The idea is to start with a first test, which gives a reference score S0, and then work on

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Le Monde puzzle [#14]

May 13, 2011
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Le Monde puzzle [#14]

Last week Le Monde puzzle (I have not received this week issue yet!) was about deriving an optimal strategy in less than 25 steps for finding the 25 answers to a binary multiple choice test, when at each trial, only the number of correct answers is known. Hence, if the correct answers are y1,…,y25, and

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Le Monde puzzle [#8]

March 29, 2011
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Le Monde puzzle [#8]

Another mathematical puzzle from Le Monde that relates to a broken calculator (skipping the useless tale): Given a pair of arbitrary positive integers (x,y) a calculator can either substract the same integer from both x and y or multiply either x or y by 2. Is it always possible to obtain equal

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Le Monde puzzle [#7]

March 26, 2011
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Le Monde puzzle [#7]

The mathematical puzzle from the weekend edition of Le Monde from a few weeks ago was not too hard to solve by induction but my R code failed miserably! The puzzle was as follows: A calculator is broken in such a way that it starts by exhibiting 0, then pressing 4, 6 or 0 keeps

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Le Monde puzzle [#6]

February 17, 2011
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Le Monde puzzle [#6]

A simple challenge in Le Monde this week: find the group of four primes such that any sum of three terms in the group is prime and the overall sum is minimised. Here is a quick exploration by simulation, using the schoolmath package (with its imperfections): A=primes(start=1,end=53) lengthA=length(A) res=4*53 for (t in 1:10^4){ B=sample(A,4,prob=1/(1:lengthA)) sto=is.prim(sum(B))

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