# Category: The Riddler

## a non-riddle

Unless I missed a point in the last riddle from the Riddler, there is very little to say about it: Given N ocre balls, N aquamarine balls, and two urns, what is the optimal way to allocate the balls to the urns towards drawing an ocre ball with no urn being empty? Both my reasoning […]

## riddles on Egyptian fractions and Bernoulli factories

Two fairy different riddles on the weekend Riddler. The first one is (in fine) about Egyptian fractions: I understand the first one as Find the Egyptian fraction decomposition of 2 into 11 distinct unit fractions that maximises the smallest fraction. And which I cannot solve despite perusing this amazing webpage on Egyptian fractions and making […]

## easy Riddler

The riddle of the week is rather standard probability calculus If N points are generated at random places on the perimeter of a circle, what is the probability that you can pick a diameter such that all of those points are on only one side of the newly halved circle? Since it is equivalent to […]

## survivalists [a Riddler’s riddle]

A neat question from The Riddler on a multi-probability survival rate: Nine processes are running in a loop with fixed survivals rates .99,….,.91. What is the probability that the first process is the last one to die? Same question with probabilities .91,…,.99 and the probability that the last process is the last one to die. […]

## numbers of numbers with numbers of their numbers

A funny riddle from The Riddler where the number of numbers that indicate the numbers of their numbers is requested. By which one means numbers like 22 (two 2’s) and 21322314 (two 1’s, three 2’s, two 3’s and one 4), the convention being that “numbers consist of alternating tallies and numerals”. And that numerals are […]

## no country for old liars

A puzzle from the Riddler about a group of five persons, A,..,E, where all and only people strictly older than L are liars, all making statements about others’ ages: A: B>20 and D>16 B: C>18 and E<20 C: D<22 and A=19 D: E≠20 and B=20 E: A>21 and C<18 The Riddler is asking for the […]

## take a random integer

A weird puzzle from FiveThirtyEight: what is the probability that the product of three random integers is a multiple of 100? Ehrrrr…, what is a random integer?! The solution provided by the Riddler is quite stunning Reading the question charitably (since “random integer” has no specific meaning), there will be an answer if there is […]

## missing digit in a 114 digit number [a Riddler’s riddle]

A puzzling riddle from The Riddler (as Le Monde had a painful geometry riddle this week): this number with 114 digits 530,131,801,762,787,739,802,889,792,754,109,70?,139,358,547,710,066,257,652,050,346,294,484,433,323,974,747,960,297,803,292,989,236,183,040,000,000,000 is missing one digit and is a product of some of the integers between 2 and 99. By comparison, 76! and 77! have 112 and 114 digits, respectively. While 99! has 156 digits. […]