mscroggs.co.uk
mscroggs.co.uk

subscribe

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:
9
"The 4th digit is 4."
"The 8th digit is 4."
4
"The 3rd digit is 1."
"The 4th digit is 7."
10
"The 11th digit is a factor of 888."
"The 11th digit is a factor of 88."
13
"The 3rd digit is 1."
"The 4th digit is 6."
23
"The 10th digit is 4."
"The 10th digit is 3."
1
"The last digit is 1, 9 or 5."
"The last digit is 1."
5
"The 3rd digit is 1."
"The 4th digit is 3."
16
"The 5th digit is 3."
"The 6th digit is 3."
11
"The sequence's length is 2+1+6."
"The sequence's length is 2×1×6."
12
"The 6th to 8th digits are 3, 3, 4."
"The 7th to 9th digits are 3, 3, 4."
2
"The 7th digit is 4."
"The 8th digit is 4."
21
"The 5th digit is 3."
"The 9th digit is 9."
22
"The 9th digit is 9."
"The 10th digit is 4."
17
"The 3rd digit is 1."
"The 4th digit is 9."
15
"The 2nd* digit is 7."
"The 1st digit is 8."
14
"The 1st digit is 7."
"The 2nd digit is 7."
7
"The last digit is not 5."
"The 4th digit is 5."
3
"The 11th digit is a factor of 10."
"The 11th digit is a factor of 321."
6
"The sequence's length is 1+9+2."
"The sequence's length is 1×9×2."
20
"The 5th digit is 3."
"The 5th digit is 4."
19
"5 does not appear."
"5 appears exactly once."
24
"The 3rd digit is 1."
"The 4th digit is 8."
25
18
"The 1st digit is 3, 7 or 8."
"The sequence's length is prime."
8
"The 3rd digit is 1."
"The 4th digit is 2."
You can view the map here.

Show answer

Archive

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

Tags

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

Archive

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