Advent calendar 2020

25 December

It's nearly Christmas and something terrible has happened: you've just landed in a town in the Arctic circle with a massive bag of letters for Santa, but you've lost to instructions for how to get to Santa's house near the north pole. You need to work out where he lives and deliver the letters to him before Christmas is ruined for everyone.
Due to magnetic compasses being hard to use near the north pole, you brought with you a special Advent compass. This compass has nine numbered directions. Santa has given the residents of the town clues about a sequence of directions that will lead to his house; but in order to keep his location secret from present thieves, he gave each resident two clues: one clue is true, and one clue is false.
Here are the clues:
"The 4th digit is 4."
"The 8th digit is 4."
"The 3rd digit is 1."
"The 4th digit is 7."
"The 11th digit is a factor of 888."
"The 11th digit is a factor of 88."
"The 3rd digit is 1."
"The 4th digit is 6."
"The 10th digit is 4."
"The 10th digit is 3."
"The last digit is 1, 9 or 5."
"The last digit is 1."
"The 3rd digit is 1."
"The 4th digit is 3."
"The 5th digit is 3."
"The 6th digit is 3."
"The sequence's length is 2+1+6."
"The sequence's length is 2×1×6."
"The 6th to 8th digits are 3, 3, 4."
"The 7th to 9th digits are 3, 3, 4."
"The 7th digit is 4."
"The 8th digit is 4."
"The 5th digit is 3."
"The 9th digit is 9."
"The 9th digit is 9."
"The 10th digit is 4."
"The 3rd digit is 1."
"The 4th digit is 9."
"The 2nd* digit is 7."
"The 1st digit is 8."
"The 1st digit is 7."
"The 2nd digit is 7."
"The last digit is not 5."
"The 4th digit is 5."
"The 11th digit is a factor of 10."
"The 11th digit is a factor of 321."
"The sequence's length is 1+9+2."
"The sequence's length is 1×9×2."
"The 5th digit is 3."
"The 5th digit is 4."
"5 does not appear."
"5 appears exactly once."
"The 3rd digit is 1."
"The 4th digit is 8."
"The 1st digit is 3, 7 or 8."
"The sequence's length is prime."
"The 3rd digit is 1."
"The 4th digit is 2."
You can view the map here.

Show answer


Show me a random puzzle
 Most recent collections 

Advent calendar 2020

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

List of all puzzles


time indices symmetry dates books combinatorics fractions remainders cryptic crossnumbers perimeter bases cryptic clues regular shapes division geometry calculus grids prime numbers balancing dodecagons ellipses sum to infinity area planes number functions coins unit fractions sequences integers chocolate odd numbers sport square numbers squares logic digital clocks crossnumber multiples quadratics polygons averages trigonometry chalkdust crossnumber 3d shapes graphs games shape menace coordinates numbers triangles cube numbers square roots chess digits probability crosswords taxicab geometry complex numbers advent irreducible numbers median lines means volume gerrymandering range rectangles algebra spheres hexagons partitions surds arrows triangle numbers tiling dice rugby angles palindromes integration crossnumbers shapes 2d shapes quadrilaterals ave speed perfect numbers addition factors differentiation sums scales mean proportion colouring clocks probabilty floors factorials folding tube maps dominos cards doubling people maths multiplication star numbers elections money christmas routes percentages circles the only crossnumber wordplay parabolas pascal's triangle products


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2021