A rather blah number Le Monde mathematical puzzle: Find all integer multiples of 11111 with exactly one occurrence of each decimal digit.. Which I solved by brute force, by looking at the possible range of multiples (and borrowing stringr:str_count from Robin!) > combien=0 > for (i in 90001:900008){ j=i*11111 combien=combien+(min(stringr::str_count(j,paste(0:9)))==1)} > combien [1] 3456 And […]

# Category: mathematical puzzle

## survivalists [a Riddlerâ€™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. […]

## Le Monde puzzle [#1092]

A Latin square Le Monde mathematical puzzle that I found rather dreary: A hidden 3×3 board contains all numbers from 1 to 9. Anselm wants to guess the board and makes two proposals. Berenicke tells him how many entries are in the right rows and colums for each proposal, along with the information that no […]

## 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 […]

## Le Monde puzzle [#1088]

A board (Ising!) Le Monde mathematical puzzle in the optimisation mode, again: On a 7×7 board, what is the maximal number of locations that one can occupy when imposing at least two empty neighbours ? Which I tried to solve by brute force and simulated annealing (what else?!), first defining a target targ=function(tabz){ sum(tabz[-c(1,9),-c(1,9)]-1.2*(tabz[-c(1,9),-c(1,9)]*tabz[-c(8,9),-c(1,9)] +tabz[-c(1,9),-c(1,9)]*tabz[-c(1,2),-c(1,9)] […]

## Le Monde puzzle [#1086]

A terse Le Monde mathematical puzzle in the optimisation mode: What is the maximal fraction of the surface of a triangle occupied by an inner triangle ABC where Abigail picks a summit A on a first side, Berenice B on a second side, and then Abigails picks C on the third side, towards Abigail maximising […]

## Le Monde puzzle [#1087]

A board-like Le Monde mathematical puzzle in the digit category: Given a (k,m) binary matrix, what is the maximum number S of entries with only one neighbour equal to one? Solve for k=m=2,…,13, and k=6,m=8. For instance, for k=m=2, the matrix is producing the maximal number 4. I first attempted a brute force random filling […]

## Le Monde puzzle [#1085]

A new Le Monde mathematical puzzle in the digit category: Given 13 arbitrary relative integers chosen by Bo, Abigail can select any subset of them to be drifted by plus or minus one by Bo, repeatedly until Abigail reaches the largest possible number N of multiples of 5. What is the minimal possible value of […]

## Le Monde puzzle [#1085]

A new Le Monde mathematical puzzle in the digit category: Given 13 arbitrary relative integers chosen by Bo, Abigail can select any subset of them to be drifted by plus or minus one by Bo, repeatedly until Abigail reaches the largest possible number N of multiples of 5. What is the minimal possible value of […]

## Le Monde puzzle [#1083]

A Le Monde mathematical puzzle that seems hard to solve without the backup of a computer (and just simple enough to code on a flight to Montpellier): Given the number N=2,019, find a decomposition of N as a sum of non-trivial powers of integers such that (a) the number of integers in the sum is […]

## missing digit in a 114 digit number [a Riddlerâ€™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. […]

## Le Monde puzzle [#1081]

A “he said-she said” Le Monde mathematical puzzle (again in the spirit of the famous Singapore high-school birthdate problem): Abigail and Corentin are both given a positive integer, a and b, such that a+b is either 19 or 20. They are asked one after the other and repeatedly if they are sure of the other’s […]

## Le Monde puzzle [#1076]

A cheezy Le Monde mathematical puzzle : (which took me much longer to find [in the sense of locating] than to solve, as Warwick U does not get a daily delivery of the newspaper [and this is pre-Brexit!]): Take a round pizza (or a wheel of Gruyère) cut into seven identical slices and turn one […]