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Puzzles

Coloured weights

You have six weights. Two of them are red, two are blue, two are green. One weight of each colour is heavier than the other; the three heavy weights all weigh the same, and the three lighter weights also weigh the same.
Using a scale twice, can you split the weights into two sets by weight?

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Advent 2018 Logic Puzzle

2018's Advent calendar ended with a logic puzzle: It's nearly Christmas and something terrible has happened: one of Santa's five helpers—Jo Ranger, Fred Metcalfe, Bob Luey, Meg Reeny, and Kip Urples—has stolen all the presents during the North Pole's annual Sevenstival. You need to find the culprit before Christmas is ruined for everyone.
Every year in late November, Santa is called away from the North Pole for a ten hour meeting in which a judgemental group of elders decide who has been good and who has been naughty. While Santa is away, it is traditional for his helpers celebrate Sevenstival. Sevenstival gets in name from the requirement that every helper must take part in exactly seven activities during the celebration; this year's available activities were billiards, curling, having lunch, solving maths puzzles, table tennis, skiing, chess, climbing and ice skating.
Each activity must be completed in one solid block: it is forbidden to spend some time doing an activity, take a break to do something else then return to the first activity. This year's Sevenstival took place between 0:00 and 10:00 (North Pole standard time).
During this year's Sevenstival, one of Santa's helpers seven activities included stealing all the presents from Santa's workshop. Santa's helpers have 24 pieces of information to give to you, but the culprit is going to lie about everything in an attempt to confuse you, so be careful who you trust.
Here are the clues:
1
Meg says: "Between 2:33 and curling, I played billiards with Jo."
15
Kip says: "The curling match lasted 323 mins."
24
Fred says: "In total, Jo and Meg spent 1 hour and 57 mins having lunch."
8
Meg says: "A total of 691 mins were spent solving maths puzzles."
17
Jo says: "I played table tennis with Fred and Meg for 2+8+5 mins."
23
Meg says: "1:32 was during my 83 min ski"
7
Meg says: "The number of mins the curling game lasted is a factor of 969."
16
Jo says: "I started skiing with Bob, and finished before Bob at 8:45."
5
Jo says: "At 4:45, Fred, Bob, Kip and I started a curling match."
14
Fred says: "I spent 135 mins playing chess with Meg."
20
Meg says: "Jo started skiing at 7:30."
4
Bob says: "I went for a 150 min ski."
13
Kip says: "Jo started skiing at 6:08."
22
Fred says: "Bob, Kip and I finished lunch at 3:30."
6
Bob says: "I played billiards with Kip from 0:00 until 1:21."
12
Fred says: "Between 3:30 and 4:45, there were 3 people climbing."
21
Fred says: "In total, Bob, Meg and I spent 269 mins ice skating."
10
Meg says: "Between 0:00 and 1:10, I was ice skating."
19
Jo says: "At 1:12, Fred and I were both in the middle of maths puzzles."
3
Jo says: "Straight after curling, I had a 108 min game of chess with Kip."
9
Fred says: "At 2:52, I started having lunch with Bob and Kip."
18
Jo says: "I spent 153 mins solving maths puzzles."
2
Fred says: "I was solving maths puzzles for 172 mins."
11
Meg says: "I spent 108 mins solving maths puzzles with Bob."

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Breaking Chocolate

You are given a bar of chocolate made up of 15 small blocks arranged in a 3×5 grid.
You want to snap the chocolate bar into 15 individual pieces. What is the fewest number of snaps that you need to break the bar? (One snap consists of picking up one piece of chocolate and snapping it into two pieces.)

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Advent 2017 logic puzzle

2017's Advent calendar ended with a logic puzzle: It's nearly Christmas and something terrible has happened: Santa and his two elves have been cursed! The curse has led Santa to forget which present three children—Alex, Ben and Carol—want and where they live.
The elves can still remember everything about Alex, Ben and Carol, but the curse is causing them to lie. One of the elves will lie on even numbered days and tell the truth on odd numbered days; the other elf will lie on odd numbered days and tell the truth on even numbered days. As is common in elf culture, each elf wears the same coloured clothes every day.
Each child lives in a different place and wants a different present. (But a present may be equal to a home.) The homes and presents are each represented by a number from 1 to 9.
Here are the clues:
21
White shirt says: "Yesterday's elf lied: Carol wants 4, 9 or 6."
10
Orange hat says: "249 is my favourite number."
5
Red shoes says: "Alex lives at 1, 9 or 6."
16
Blue shoes says: "I'm the same elf as yesterday. Ben wants 5, 7 or 0."
23
Red shoes says: "Carol wants a factor of 120. I am yesterday's elf."
4
Blue shoes says: "495 is my favourite number."
15
Blue shoes says: "Carol lives at 9, 6 or 8."
22
Purple trousers says: "Carol wants a factor of 294."
11
White shirt says: "497 is my favourite number."
6
Pink shirt says: "Ben does not live at the last digit of 106."
9
Blue shoes says: "Ben lives at 5, 1 or 2."
20
Orange hat says: "Carol wants the first digit of 233."
1
Red shoes says: "Alex wants 1, 2 or 3."
24
Green hat says: "The product of the six final presents and homes is 960."
17
Grey trousers says: "Alex wants the first digit of 194."
14
Pink shirt says: "One child lives at the first digit of 819."
3
White shirt says: "Alex lives at 2, 1 or 6."
18
Green hat says: "Ben wants 1, 5 or 4."
7
Green hat says: "Ben lives at 3, 4 or 3."
12
Grey trousers says: "Alex lives at 3, 1 or 5."
19
Purple trousers says: "Carol lives at 2, 6 or 8."
8
Red shoes says: "The digits of 529 are the toys the children want."
13
Green hat says: "One child lives at the first digit of 755."
2
Red shoes says: "Alex wants 1, 4 or 2."

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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:
10
None of the digits of 171 is the location.
3
None of the digits of 798 is the motive.
7
One of the digits of 691 is the location.
16
None of the digits of 543 is the location.
5
One of the digits of 414 is the murderer.
20
The first digit of 287 is the number of false red clues.
8
Clues on days that are factors of 768 are all true.
22
The murderer is the square root of one of the digits of 191.
11
One of the digits of 811 is the weapon.
19
The highest common factor of the weapon and 128 is 1.
13
None of the digits of 512 is the murderer.
18
One of the digits of 799 is the motive.
17
None of the digits of 179 is the motive.
6
None of the digits of 819 is the location.
24
One of the digits of 319 is total number of false clues.
23
One of the digits of 771 is the murderer.
2
The weapon is not one of the digits of 435.
14
The final digit of 415 is the number of true blue clues.
4
The weapon is a factor of 140.
12
The number of false clues before today is the first digit of 419.
9
One of the digits of 447 is the motive.
1
None of the digits of 563 is the motive.
21
One of the digits of 816 is the murderer.
15
One of the digits of 387 is the motive.

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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.

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Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

Sunday Afternoon Maths LXV

Cryptic crossnumber #1
Breaking Chocolate
Square and cube endings

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