There is a wall along the five metre and three metre sides.

A friend sometimes brings their dog and we sit with a drink putting the world to rights.

However, we are a bit concerned about the dog falling off the decking. What is the longest piece of rope that we can use to tie the dog so it can just reach the edge, but not fall off?

The path described by the end of the rope is an arc of a circle, and the longest possible rope will make an arc with the diagonal side as a tangent to the arc.

Assuming the rope is tied in the corner between the five metre and three metre sides, we have a right angled triangle with a three metre hypotenuse.

Imagine another triangle that forms the part of the trapezium that isn't the two metre by five metre rectangle. This is a right angled triangle with a common angle with the first triangle - similar triangles.

Tan of the smallest angle in the second triangle is 1/5, so the angle is Arctan (1/5) = 0.157079633 radians.

Returning to the first triangle the length of the rope is 3 * Cos x = 3 * 0.98768834054 which is about 2.96 metres.

]]>There is a wall along the five metre and three metre sides.

A friend sometimes brings their dog and we sit with a drink putting the world to rights.

However, we are a bit concerned about the dog falling off the decking. What is the longest piece of rope that we can use to tie the dog so it can just reach the edge, but not fall off?

As usual you can post your suggested answers as a comment on this website, reply to the post on Facebook, or retweet or reply on Twitter @quizmastershop.

Answer at 9.00 on Monday

]]>1. The perpendicular pronoun

I

2. The ratio of a circle's circumference to its diameter

PI

3. Nickname of former Speaker of the House Thomas P. O'Neill

TIP

4. A narrow piece of land formed by longshore drift

SPIT

5. Walks or runs with quick light steps

TRIPS

6. Alternative term for handwriting

SCRIPT

7. Muscle having three points of attachment

TRICEPS

8. An archaic word for Recipes

RECEIPTS

9. The most spine-chilling

CREEPIEST

10. Central points of earthquakes

EPICENTRES

Pleasingly each successive answer starts with a different letter, and is a "proper" anagram of the previous answer.

]]>1. The perpendicular pronoun

2. The ratio of a circle's circumference to its diameter

3. Nickname of former Speaker of the House Thomas P. O'Neill

4. A narrow piece of land formed by longshore drift

5. Walks or runs with quick light steps

6. Alternative term for handwriting

7. Muscle having three points of attachment

8. An archaic word for Recipes

9. The most spine-chilling

10. Central points of earthquakes

As usual you can post your suggested answers as a comment on this website, reply to the post on Facebook, or retweet or reply on Twitter @quizmastershop.

Answer at 9.00 on Monday

]]>1. T HS H LTH VN T HRG DSB FRM

Thou Shalt Have No Other Gods Before Me

2. THS HL TNTM KNT THN YG RVNM G

Thou Shalt Not Make Unto Thee Any Graven Image

3. TH SH LTN TT KTHN MFT HLRD THY G DNVN

Thou Shalt Not Take The Name Of The Lord Thy God In Vain

4. R MM BRT HS BBT HDY TKP THLY

Remember The Sabbath Day To Keep It Holy

5. HN RTHYF THRN D THYM THR

Honour Thy Father And Thy Mother

6. T HSH L TNTM RDR

Thou Shalt Not Murder

7. TH S HLTN TCM MTDL TRY

Thou Shalt Not Commit Adultery

8. THS H LTNTS TL

Thou Shalt Not Steal

9. T HS HL TN TB RFL SWT NS SG NST THYNG HBR

Thou Shalt Not Bear False Witness Against The Neighbour

10. TH SH LT NT CV T

Thou Shalt Not Covet

These being the Ten Commandments

]]>1. T HS H LTH VN T HRG DSB FRM

2. THS HL TNTM KNT THN YG RVNM G

3. TH SH LTN TT KTHN MFT HLRD THY G DNVN

4. R MM BRT HS BBT HDY TKP THLY

5. HN RTHYF THRN D THYM THR

6. T HSH L TNTM RDR

7. TH S HLTN TCM MTDL TRY

8. THS H LTNTS TL

9. T HS HL TN TB RFL SWT NS SG NST THYNG HBR

10. TH SH LT NT CV T

As usual you can post your suggested answers as a comment on this website, reply to the post on Facebook, or retweet or reply on Twitter @quizmastershop.

Answer at 9.00 on Monday

]]>Clearly there is a problem.

Can you see a solution using a little "creative" arithmetic?

The solution is to lend a horse to the sons, so now they have 18. The first son gets nine (a half), the second son gets six (a third) and the third son gets two (a ninth). Nine plus six plus two is 17, and they can return the loaned horse to you.

Yes, it is dodgy!

And if you can, what about another farmer who has horses and leaves one seventh of the horses to his youngest son, instead of one ninth.

Assuming the same creative solution works in this case, how many horses does the farmer have?

In this case

$$ 1/2 + 1/3 + 1/7 = 41/42 $$

So the farmer has 41 horses.

]]>Clearly there is a problem.

Can you see a solution using a little "creative" arithmetic?

And if you can, what about another farmer who has horses and leaves one seventh of the horses to his youngest son, instead of one ninth.

Assuming the same creative solution works in this case, how many horses does the farmer have?

Answer at 10.00 on Monday

]]>Click to see the Sample Rounds or Buy Your Quiz and get started.

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LINKS: “THE GENT & US” A 20th Century Link

1 No longer in clinical use, the analgesic and anaesthetic drug with the formula C12H25N.HCl is abused as a hallucinogen and referred to informally as “angel dust” – what is its three-letter abbreviation?

Answer - PCP

2 Countdown Conundra: (a) NEON GRILL and (b) ALPINE SUN rearrange to which English 9-letter words? LINK (middle parts of) 1,2(a)&2(b)

Answers - (a) ENROLLING (b) PENINSULA

Link - C + OLL +INS (Michael Collins)

3 Constellations: if Auriga is The Charioteer, Canis Major is The Big Dog and Ursa Minor is The Little Bear, what is Aquila?

Answer - THE EAGLE (has landed)

4 (a) Released 50 years ago on July 11th, which signature song by a cult figure who died in 2016 was inspired by a Stanley Kubrick film of the previous year? (b) What are the song’s first two words?

Answers - (a) SPACE ODDITY (b) GROUND CONTROL

5 I am a member of a current British political party that adopted the bird of liberty as its logo in 1988 after a series of identity and name changes … so I am a what (two non-abbreviated words, keep it clean please)? LINK 5&6

Answer - LIBERAL DEMOCRAT

6 Which Arthurian knight who went in search of the Holy Grail is eponymously the title of a Romantic opera by Richard Wagner?

Answer - LOHENGRIN

Link - ALD + RIN (Buzz Aldrin)

7 (a) Which Greek deity was the god of the Sun? (b) Which Roman deity was the goddess of the Moon?

Answers - (a) APOLLO (b) DIANA

8 What four-letter word can mean any of the following: a racing yacht of between 15 and 20 metres in length; an Austin car model produced between 1969 and 1981; a skirt, coat or dress that reaches down to the ankle? LINK 7(a)&8

Answer - MAXI

Link - Apollo XI

9 With the “real” first name Archibald, which iconic Emmerdale character was played by Stan Richards from 1978 until 2004?

Answer - SETH ARMSTRONG (Neil Armstrong)

10 How is the denary number “3” written in binary form? LINK 7(a)&10

Answer - 11

Two thematic phrases are spelt out by (a) the initial letters; (b) the last letters of the ten answers, reading upwards.

1 SMALL STEP (for The Gent)

1 GIANT LEAP (for Us)

]]>Your challenge is to work out the largest number of Chicken McNuggets that it is not possible to buy. That is, by purchasing any number of each of the four box sizes, in any combination, what is the largest number that you cannot buy.

Clearly you cannot buy one, two or three. Four is one box of four, but five is not possible. Six is one box of six, but seven is not possible. Eight is two boxes of four, nine is a box of nine, and ten is a box of four and a box of six.

Eleven cannot be done.

Twelve is two boxes of six, 13 is a box of four and a box of nine, 14 is two boxes of four and a box of six, and fifteen is a box of six and a box of nine.

We have now made four consecutive numbers of McNuggets and the smallest box contains four. So we can make any number by adding one or more boxes of four to twelve, 13, 14 or 15.

So eleven is the largest number of McNuggets it is not possible to buy.

Before the box of four McNuggets was introduced, things were much harder.

The answer in this case is 43. We will leave you to work out the list of numbers that can and cannot be made, as above, if you so wish.

To show that this is the highest number of McNuggets that used to be unbuyable:

44 = 6 + 9 + 9 + 20

45 = 5 * 9

46 = 6 + 20 + 20

47 = 3 * 9 + 20

48 = 6 + 6 + 4 * 9

49 = 9 + 20 + 20

So now we have six consecutive numbers and six is the smallest box, so we can make any number by adding one or more boxes to one of these six.

Generally, the largest number that can't be made from a set of other numbers is called the Frobenius number. The specific problem with McNuggets was devised by Henri Picciotto in a McDonalds, presumably whilst eating Chicken McNuggets.

]]>LINKS: “THE GENT & US” A 20th Century Link

1 No longer in clinical use, the analgesic and anaesthetic drug with the formula C12H25N.HCl is abused as a hallucinogen and referred to informally as “angel dust” – what is its three-letter abbreviation?

2 Countdown Conundra: (a) NEON GRILL and (b) ALPINE SUN rearrange to which English 9-letter words? LINK (middle parts of) 1,2(a)&2(b)

3 Constellations: if Auriga is The Charioteer, Canis Major is The Big Dog and Ursa Minor is The Little Bear, what is Aquila?

4 (a) Released 50 years ago on July 11th, which signature song by a cult figure who died in 2016 was inspired by a Stanley Kubrick film of the previous year? (b) What are the song’s first two words?

5 I am a member of a current British political party that adopted the bird of liberty as its logo in 1988 after a series of identity and name changes … so I am a what (two non-abbreviated words, keep it clean please)? LINK 5&6

6 Which Arthurian knight who went in search of the Holy Grail is eponymously the title of a Romantic opera by Richard Wagner?

7 (a) Which Greek deity was the god of the Sun? (b) Which Roman deity was the goddess of the Moon?

8 What four-letter word can mean any of the following: a racing yacht of between 15 and 20 metres in length; an Austin car model produced between 1969 and 1981; a skirt, coat or dress that reaches down to the ankle? LINK 7(a)&8

9 With the “real” first name Archibald, which iconic Emmerdale character was played by Stan Richards from 1978 until 2004?

10 How is the denary number “3” written in binary form? LINK 7(a)&10

Two thematic phrases are spelt out by (a) the initial letters; (b) the last letters of the ten answers, reading upwards.

Answer at 10.00 on Monday

]]>Your challenge is to work out the largest number of Chicken McNuggets that it is not possible to buy. That is, by purchasing any number of each of the four box sizes, in any combination, what is the largest number that you cannot buy.

Now that isn't too hard, so once you have solved that, what was the largest number of Chicken McNuggets that you could not buy before the box of four in the Happy Meal was introduced.

Answer at 9.00 on Monday

]]>The children were going to do some potato prints, and a keen Teaching Assistant had prepared the potatoes for the children. Unfortunately she had not read the lesson plan and there were two problems.

Firstly, there were twice as many children as potatoes.

This was easily solved, we thought, just cut each potato in half.

Well yes, the potatoes would need to be cut in half; however, the Teaching Assistant had cut the potatoes into cubes, and the children were going to print hexagons.

The challenge was how to cut each cube in half, with one cut, to leave both halves with a hexagonal face.

Were we able to help, and if so, how?

As you might guess from our posting this puzzle, we were able to help.

Make a cut that passes through the midpoints of six of the edges and you will have your hexagons.

]]>The children were going to do some potato prints, and a keen Teaching Assistant had prepared the potatoes for the children. Unfortunately she had not read the lesson plan and there were two problems.

Firstly, there were twice as many children as potatoes.

This was easily solved, we thought, just cut each potato in half.

Well yes, the potatoes would need to be cut in half; however, the Teaching Assistant had cut the potatoes into cubes, and the children were going to print hexagons.

The challenge was how to cut each cube in half, with one cut, to leave both halves with a hexagonal face.

Were we able to help, and if so, how?

Answer at 9.00 on Monday

]]>The four phrases were

*Grandmother in Caernarfon*

*Dislike within the sound of Bow Bells*

*You in Ancient Rome*

*Warning on a Golf Course*

The Welsh for Grandmother in North Wales (hence Caernarfon) is Nain - pronounced Nine.

Cockneys are renowned for dropping aitches, and so Hate would become 'Ate - pronounced Eight.

The second person singular in Latin is Tu - pronounced Two.

And the warning on a golf course is Fore - pronounced Four.

And so all of these are Homophones of Numbers

]]>You will see four phrases, one at a time. The first is here, the second is here, the third is here, and the last one is below. You have to work out the connection between the four phrases. Obviously, the more that you see, the easier it should be.

The fourth one is:

*Warning on a Golf Course*

Answer at 9.00 on Monday

]]>You will see four phrases, one at a time. The first is here, the second is here, the third is below, and the last one will be revealed in an hour. You have to work out the connection between the four phrases. Obviously, the more that you see, the easier it should be.

The third one is:

*You in Ancient Rome*

Answer at 9.00 on Monday

]]>You will see four phrases, one at a time. The first is here, the second is below, and the other two will be revealed at hourly intervals. You have to work out the connection between the four phrases. Obviously, the more that you see, the easier it should be.

The second one is:

*Dislike within the sound of Bow Bells*

Answer at 9.00 on Monday

]]>You will see four phrases, one at a time. The first is below, and the other three will be revealed at hourly intervals. You have to work out the connection between the four phrases. Obviously, the more that you see, the easier it should be.

The first one is:

*Grandmother in Caernarfon*

Answer at 9.00 on Monday

]]>One evening, when an extremely popular quiz night is taking place in the Jolly Quiz Master Arms, the hotel is fully booked. Unfortunately the Quiz Master at the quiz night had forgotten to make a reservation.

How did the hotel fit him in?

The hotel manager instructed all the guests to move to the room with a number one greater than their current room. So the guest in room one moved to room two, the guest in room two moved to room three, and so on with the guest in room n moving to room n+1.

As the hotel has an infinite number of rooms this can be done without a problem, and room one is now free for the Quiz Master.

This was accomplished and the Quiz Master had a room for the night, but the hotel's problems were far from over.

The quiz nights in the the Jolly Quiz Master Arms are very popular, and Infinity Quiz Tours arrived with a party of quiz enthusiasts. The bus held an infinite number of people destined for the quiz night, and all needing a room.

How did the hotel fit them all in?

This time the hotel manager instructed all the guests to move to the room with a number twice that of their current room. So the guest in room one moved to room two, the guest in room two moved to room four, and so on with the guest in room n moving to room 2n.

Then the hotel manager instructed all the passengers to go to the room with a number twice their seat number minus one. So the passenger in seat one went to room one, the passenger in seat two went to room three, and so on with the passenger in room n going to room 2n-1.

This was originally published by David Hilbert as The Paradox of the Grand Hotel

]]>One evening, when an extremely popular quiz night is taking place in the Jolly Quiz Master Arms, the hotel is fully booked. Unfortunately the Quiz Master at the quiz night had forgotten to make a reservation.

How did the hotel fit him in?

This was accomplished and the Quiz Master had a room for the night, but the hotel's problems were far from over.

The quiz nights in the the Jolly Quiz Master Arms are very popular, and Infinity Quiz Tours arrived with a party of quiz enthusiasts. The bus held an infinite number of people destined for the quiz night, and all needing a room.

How did the hotel fit them all in?

Answer at 9.00 on Monday

]]>Midsummer Day is not the same as the Summer Solstice, but is often confused (or conflated) with it.

The Quarter Days were the days on which rents, taxes etc. were to be paid.

The first of them (Lady Day) is still the day on which the UK Tax Year starts, albeit the date has moved to 6th April when such things moved eleven days at the change from the Julian to the Gregorian calendar.

]]>Every hour it gains 36 minutes.

It was set correctly at 2 o'clock in the morning.

Exactly one hour ago it stopped and the time displayed is 24 minutes past eight in the morning.

What time is it now?

As the clock was correct at 2.00 AM it has added six hours and 24 minutes, or 384 minutes.

For each real hour the clock adds on 96 minutes (it gains 36 minutes every hour) and 384 divided by 96 equals 4. So the clock was running for four hours and stopped at 6.00 AM.

As it stopped one hour ago it is now 7 o'clock in the morning.

Of course, that assumes it stopped the same day that it was set. Had it stopped the following day it would have added another 24 hours. This is 1,440 minutes which, divided by 96 gives 15 hours. So the clock would have stopped 15 hours later, that is 21.00, and the time is now 10.00 PM.

This process can be repeated if you wish, adding 15 hours per day

]]>Every hour it gains 36 minutes.

It was set correctly at 2 o'clock in the morning.

Exactly one hour ago it stopped and the time displayed is 24 minutes past eight in the morning.

What time is it now?

Answer at 9.00 on Monday

]]>There are ten teams in the competition, and in the group stage every team plays the other nine teams once. So at the end of the group stage all the teams will have played nine matches.

For each win the team gets two points, for a loss the team gets zero points, and for a tie (or no result - don't worry about it) the team gets one point. If two teams are level on points the team with the best net run rate (again don't worry about it) is placed higher.

The top four teams in the table at the end of the group stage qualify for the semifinals.

The questions are:

- What is the highest number of points that a team can get and not qualify for the semifinals?
- What is the lowest number of points that a team can get and still qualify for the semifinals?

In the first question we are looking at a situation where the top five teams are level on points, and with the highest number of points they can get. This means that the top five teams must win all their matches against the bottom five teams. So they all have five wins, which gives ten points.

In addition, all of the top five teams have four games against the other teams in the top five. The simplest way to imagine this is if all these games are tied, and each team gains four points for four ties.

These four points added to the ten points from the five wins above gives 14 points. So a team could fail to qualify with 14 points.

In the second question we are looking at a situation where the bottom seven teams are level on points, and with the lowest number of points they can get. This means that the top three teams must win all their matches against the bottom seven teams. So the bottom seven all have three losses, which gives zero points.

In addition, all of the bottom seven teams have six games against the other teams in the bottom seven. The simplest way to imagine this is if all these games are tied, and each team gains six points for six ties.

So a team could qualify with six points.

]]>There are ten teams in the competition, and in the group stage every team plays the other nine teams once. So at the end of the group stage all the teams will have played nine matches.

For each win the team gets two points, for a loss the team gets zero points, and for a tie (or no result - don't worry about it) the team gets one point. If two teams are level on points the team with the best net run rate (again don't worry about it) is placed higher.

The top four teams in the table at the end of the group stage qualify for the semifinals.

The questions are:

- What is the highest number of points that a team can get and not qualify for the semifinals?
- What is the lowest number of points that a team can get and still qualify for the semifinals?

Answer at 9.00 on Monday

]]>Start both timers as the egg goes into the boiling water.

When the seven-minute hourglass completes, turn it over.

When the eleven-minute hourglass completes, turn the seven-minute hourglass over.

When the seven-minute hourglass completes, take out the egg.

]]>Answer at 9.00 on Monday

]]>Placing a decimal point between them produces 1.2, which is greater than 1 and less than 2.

Also, a square root sign gives 1.41421356237 (approximately) which meets the criteria.

]]>