Posts Tagged ‘ mathematical puzzle ’

Le Monde puzzle [#1036]

January 3, 2018
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Le Monde puzzle [#1036]

An arithmetic Le Monde mathematical puzzle to conclude 2017: Find (a¹,…,a¹³), a permutation of (1,…,13) such that a¹/a²+a³=a²+a³/a³+a⁴+a⁵=b¹<1 a⁶/a⁶+a⁷=a⁶+a⁷/a⁷+a⁸+a⁹=a⁷+a⁸+a⁹/a⁵+a⁹+a¹⁰=b²<1 a¹¹+a¹²/a¹²+a¹³=a¹²+a¹³/a¹³+a¹⁰=b³<1 The question can be solved by brute force simulation, checking all possible permutations of (1,…,13). But 13! is 6.6 trillion, a wee bit too many cases. Despite the problem being made of only four constraints […]

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cyclic riddle [not in NYC!]

December 28, 2017
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cyclic riddle [not in NYC!]

In the riddle of this week on fivethirtyeight, the question is to find the average number of rounds when playing the following game: P=6 players sitting in a circle each have B=3 coins and with probability 3⁻¹ they give one coin to their right or left side neighbour, or dump the coin to the centre. […]

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Le Monde puzzle [#1033]

December 18, 2017
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Le Monde puzzle [#1033]

A simple Le Monde mathematical puzzle after two geometric ones I did not consider: Bob gets a 2×3 card with three integer entries on the first row and two integer entries on the second row such that (i) entry (1,1) is 1, (ii) summing up subsets of adjacent entries produces all integers from 1 to […]

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Le Monde [last] puzzle [#1026]

November 1, 2017
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Le Monde [last] puzzle [#1026]

The last and final Le Monde puzzle is a bit of a disappointment, to wit: A 4×4 table is filled with positive and different integers. A 3×3 table is then deduced by adding four adjacent [i.e. sharing a common corner] entries of the original table. Similarly with a 2×2 table, summing up to a unique […]

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splitting a field by annealing

October 17, 2017
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splitting a field by annealing

A recent riddle [from The Riddle] that I pondered about during a [long!] drive to Luxembourg last weekend was about splitting a square field into three lots of identical surface for a minimal length of separating wire… While this led me to conclude that the best solution was a T like separation, I ran a […]

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Le Monde puzzle [#1021]

September 17, 2017
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Le Monde puzzle [#1021]

A puzzling Le Monde mathematical puzzle for which I could find no answer in the allotted time!: A most democratic electoral system allows every voter to have at least one representative by having each of the N voters picking exactly m candidates among the M running candidates and setting the size n of the representative […]

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Le Monde puzzle [#1020]

September 14, 2017
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Le Monde puzzle [#1020]

A collection of liars in this Le Monde mathematical puzzle: A circle of 16 liars and truth-tellers is such that everyone states that their immediate neighbours are both liars. How many liars can there be? A circle of 12 liars and truth-tellers is such that everyone state that their immediate neighbours are one liar plus […]

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Le Monde puzzle [#1018]

August 28, 2017
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Le Monde puzzle [#1018]

An arithmetic Le Monde mathematical puzzle (that first did not seem to involve R programming because of the large number of digits in the quantity involved): An integer x with less than 100 digits is such that adding the digit 1 on both sides of x produces the integer 99x.  What are the last nine […]

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sequence riddle

August 9, 2017
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sequence riddle

The riddle this week on The Riddler was about finding the largest sequence of integers between 1 and 100 such that each integer is only used once and always followed by a multiple or a factor. A basic R code searching at random [and programmed during a massive downpour on Skye] led to a solution […]

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Le Monde puzzle [#1707]

July 27, 2017
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Le Monde puzzle [#1707]

A geometric Le Monde mathematical puzzle: Given a pizza of diameter 20cm, what is the way to cut it by two perpendicular lines through a point distant 5cm from the centre towards maximising the surface of two opposite slices?  Using the same point as the tip of the four slices, what is the way to […]

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