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Turning Squares

Each square on a chessboard contains an arrow point up, down, left or right. You start in the bottom left square. Every second you move one square in the direction shown by the arrow in your square. Just after you move, the arrow on the square you moved from rotates 90° clockwise. If an arrow would take you off the edge of the board, you stay in that square (the arrow will still rotate).
You win the game if you reach the top right square of the chessboard. Can I design a starting arrangement of arrows that will prevent you from winning?

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Advent 2016 Murder Mystery

2016's Advent calendar ended with a murder mystery, with each of the murderer, motive, weapon and location being a digit from 1 to 9. Here are the clues:
None of the digits of 171 is the location.
None of the digits of 798 is the motive.
One of the digits of 691 is the location.
None of the digits of 543 is the location.
One of the digits of 414 is the murderer.
The first digit of 287 is the number of false red clues.
Clues on days that are factors of 768 are all true.
The murderer is the square root of one of the digits of 191.
One of the digits of 811 is the weapon.
The highest common factor of the weapon and 128 is 1.
None of the digits of 512 is the murderer.
One of the digits of 799 is the motive.
None of the digits of 179 is the motive.
None of the digits of 819 is the location.
One of the digits of 319 is total number of false clues.
One of the digits of 771 is the murderer.
The weapon is not one of the digits of 435.
The final digit of 415 is the number of true blue clues.
The weapon is a factor of 140.
The number of false clues before today is the first digit of 419.
One of the digits of 447 is the motive.
None of the digits of 563 is the motive.
One of the digits of 816 is the murderer.
One of the digits of 387 is the motive.

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Tags: logic, advent

Hat Check

Three logicians, A, B and C, are wearing hats. Each has a strictly positive integer written on it. The number on one of the hats is the sum of the numbers on the other two.
The logicians say:
A: I don't know the number on my hat.
B: The number on my hat is 15.
Which numbers are on hats A and C?

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Tags: logic

The Self Referential Crossword

Fill in the following crossnumber grid so that each clue describes the solution.
For example, if some clues read "TEN DS", "ONE X" and "THREE ES" then there will be ten Ds, one X and three Es in the completed grid. The entries in the crossword include the spaces.


In the grid below, there are 12 holes hidden in the grid. Each of the arrows is pointing towards at least one hole. None of the arrows covers a hole.
For example, the arrow in the first row tells you that at least one of the last four squares in that row contains a hole.
Find the location of all 12 holes.
Tags: logic

Dice Maze

Source: Daily Telegraph, 30/05/2015
Each colour represents a different direction (up, down, left or right) and the number of dots on each die tells you how far to go. Starting at the middle die, following the directions correctly will cause you to visit every die exactly once.

Which die will you visit last on the journey?

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Tags: logic


Messrs. Banker, Dentist, Apothecary and Scrivener played whist last night. (whist is a four player card game where partners sit opposite each other.) Each of these gentlemen is the namesake of another's vocation.
Last night, the apothecary partnered Mr. Apothecary; Mr. Banker's partner was the scrivener; on Mr. Scrivener's right sat the dentist.
Who sat on the banker's left?

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Tags: Logic, Cards
© Matthew Scroggs 2017