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Le Monde puzzle [#1073]

November 2, 2018
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Le Monde puzzle [#1073]

And here is Le Monde mathematical puzzle  last competition problem Find the number of integers such that their 15 digits are all between 1,2,3,4, and the absolute difference between two consecutive digits is 1. Among these numbers how many have 1 as their three-before-last digit and how many have 2? Combinatorics!!! While it seems like

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Le Monde puzzle [#1072]

October 30, 2018
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Le Monde puzzle [#1072]

The penultimate Le Monde mathematical puzzle  competition problem is once again anti-climactic and not worth its points: For the figure below , describing two (blue) half-circles intersecting with a square of side 20cm, and a (orange) quarter of a circle with radius 20cm, find the radii of both gold circles, respectively tangent

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ABC intro for Astrophysics

October 15, 2018
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ABC intro for Astrophysics

Today I received in the mail a copy of the short book published by edp sciences after the courses we gave last year at the astrophysics summer school, in Autrans. Which contains a quick introduction to ABC extracted from my notes (which I still hope to turn into a book!). As well as a longer

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Le Monde puzzle [#1070]

October 10, 2018
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Le Monde puzzle [#1070]

Rewording Le Monde mathematical puzzle  fifth competition problem For the 3×3 tables below, what are the minimal number of steps to move from left to rights when the yellow tokens can only be move to an empty location surrounded by two other tokens? In the 4×4 table below, there are 6 green tokens. How many

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Le Monde puzzle [#1066]

October 2, 2018
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Le Monde puzzle [#1066]

A purely (?) algorithmic Le Monde mathematical puzzle For the table below, what is the minimal number of steps required to reach equal entries when each step consists in adding ones to three entries sitting in a L, such as (7,11,12) or (5,6,10)? Same question for the inner table of four in yellow. For the

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Le Monde puzzle [#1068]

September 25, 2018
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Le Monde puzzle [#1068]

And here is the third Le Monde mathematical puzzle  open for competition: Consider for this puzzle only integers with no zero digits. Among these an integer x=a¹a²a³… is refined if it is a multiple of its scion, the integer defined as x without the first digit, y=a²a³…. Find the largest refined integer x such the

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Le Monde puzzle [#1066]

September 18, 2018
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Le Monde puzzle [#1066]

The second Le Monde mathematical puzzle in the new competition is sheer trigonometry: When in the above figures both triangles ABC are isosceles and the brown segments are all of length 25cm, find the angle in A and the value of DC², respectively. This could have been solved by R coding the various possible angles

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Le Monde puzzle [#1066]

September 12, 2018
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Le Monde puzzle [#1066]

Recalling Le Monde mathematical puzzle  first competition problem For the X table below, what are the minimal number of lights that are on (green) to reach the minimal and maximal possible numbers of entries (P) with an even (P as pair) number of neighbours with lights on? In the illustration below, there are 16 lights

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riddles on a line [#2]

September 10, 2018
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riddles on a line [#2]

A second Riddle(r), with a puzzle related with the integer set Ð={,12,3,…,N}, in that it summarises as Given a random walk on Ð, starting at the middle N/2, with both end states being absorbing states, and a uniform random move left or right of the current value to the (integer) middle of the corresponding (left

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Le Monde puzzle [#1650]

September 5, 2018
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Le Monde puzzle [#1650]

A penultimate Le Monde mathematical puzzle  before the new competition starts For a game opposing 40 players over 12 questions, anyone answering correctly a question gets as reward the number of people who failed to answer. Alice is the single winner: what is her minimal score? In another round, Bob is the only lowest

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