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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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ABC in Montréal

September 3, 2018
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ABC in Montréal

There will be a symposium on ABC in Montréal this coming December, the day before NIPS, in a continuation of past years NIPS workshops. While invited speakers and panelists have been selected by the committee, a call for papers is open. Note that in continuation with the best “ABC in…” tradition, registration is free! I

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IMS workshop [day 3]

August 29, 2018
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IMS workshop [day 3]

I made the “capital” mistake of walking across the entire NUS campus this morning, which is quite green and pretty, but which almost enjoys an additional dimension brought by such an intense humidity that one feels having to get around this humidity!, a feature I have managed to completely erase from my memory of my

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riddles on a line

August 21, 2018
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riddles on a line

In the Riddler of August 18, two riddles connected with the integer set Ð={2,3,…,10}: Given a permutation of Ð, what is the probability that the most likely variation (up or down) occurs at each term? Given three players choosing three different integers in Ð sequentially, and rewards in Ð allocated to the closest of the

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approximative Laplace

August 17, 2018
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approximative Laplace

I came across this question on X validated that wondered about one of our examples in Monte Carlo Statistical Methods. We have included a section on Laplace approximations in the Monte Carlo integration chapter, with a bit of reluctance on my side as this type of integral approximation does not directly connect to Monte Carlo

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Le Monde puzzle [#1063]

August 8, 2018
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Le Monde puzzle [#1063]

A simple (summertime?!) arithmetic Le Monde mathematical puzzle A “powerful integer” is such that all its prime divisors are at least with multiplicity 2. Are there two powerful integers in a row, i.e. such that both n and n+1 are powerful?  Are there odd integers n such that n² – 1 is a powerful integer

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Le Monde puzzle [#1062]

July 27, 2018
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Le Monde puzzle [#1062]

A simple Le Monde mathematical puzzle none too geometric: Find square triangles which sides are all integers and which surface is its perimeter. Extend to non-square rectangles. No visible difficulty by virtue of Pythagore’s formula: for (a in 1:1e4) for (b in a:1e4) if (a*b==2*(a+b+round(sqrt(a*a+b*b)))) print(c(a,b)) produces two answers 5 12 6 8 and in

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