- 90 D in a RA
- 6 L on a W
- 64 S on a CB
- 1 FS 2 FJ
- S 1 YF a GTL

S 2 SF in LWY

S 3 YK and HHT - 3600 S in an H
- 15 Z in a Q
- 12 D of C
- 3 C is 27
- 4 P in a SQ

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

]]>The same applies with 15,873 and 7y, and 8,547 and 13y.

These are known as Magic Numbers.

The puzzle is to find the smallest Magic Number for 17. That is the smallest number that when multiplied by 17y produces a number in which every digit is y.

To find this number try to divide 17 into 111, 1,111, 11,111 and so on until you find one with no remainder. That is, the smallest number of the pattern 111 . . . 111 that is a multiple of 17.

The number is 1,111,111,111,111,111 and the number is 65,359,477,124,183. That is, 65,359,477,124,183 x 17 = 1,111,111,111,111,111.

So the answer is 65,359,477,124,183

]]>The same applies with 15,873 and 7y, and 8,547 and 13y.

These are known as Magic Numbers.

The puzzle is to find the smallest Magic Number for 17. That is the smallest number that when multiplied by 17y produces a number in which every digit is y.

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

]]>If 2019 teams enter a knockout competition, how many matches are needed to produce a winner. Assume that each match is played to a finish, with extra time, sudden death extra time and then a kicking competition to decide the winner - as is the case in the Rugby World Cup knockout matches.

As each match eliminates one team and we need one winner, we need to eliminate 2018 of the 2019 team, meaning 2018 matches.

]]>

If 2019 teams enter a knockout competition, how many matches are needed to produce a winner. Assume that each match is played to a finish, with extra time, sudden death extra time and then a kicking competition to decide the winner - as is the case in the Rugby World Cup knockout matches.

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

]]>In the quarter finals the top teams in each of the groups play a game against the second-placed team from another group.

The winners of the four quarter-final games progress to the semi finals, and the four losers play no further matches.

In the semi finals, the two winners progress to the final, with the winners of the final becoming World Champions; the two losers play a Third-Fourth play off.

The questions is, what is the largest number of teams that can finish the tournament having lost exactly one game?

Here is an amazing answer by Thomas Cappleman

In the group stages, in one group one team beats all the other four teams, and the other four teams draw their games with each other. In the other three groups A beats B, B beats C and D beats E, and the other games are drawn.

This means the eight teams in the quarter finals have all lost zero games, apart from one team that has lost one game.

The other 12 teams have a record of Played 4, Won 0, Drawn 3, Lost 1. And they leave the tournament

Of the eight teams in the quarter finals:

One will lose no further games (the winners) and this is the team that has already lost one game, so they finish on one loss.

One team will lose two games (the team that comes fourth).

The others all lose one further game and these are the unbeaten teams, so they end on one loss too.

This means that a total of 19 teams finish the tournament having lost exactly one game. The only team that doesn't is the team that comes fourth - unbelievable!

]]>In the quarter finals the top teams in each of the groups play a game against the second-placed team from another group.

The winners of the four quarter-final games progress to the semi finals, and the four losers play no further matches.

In the semi finals, the two winners progress to the final, with the winners of the final becoming World Champions; the two losers play a Third-Fourth play off.

The questions is, what is the largest number of teams that can finish the tournament having lost exactly one game?

First here is our solution, which we thought was good.

In the group stages, in each group one team beats all the other four teams, and the other four teams draw their games with each other. [An unlikely scenario, it is true, but it is possible]

This means the four group winners have a record of Played 4, Won 4, Lost 0. The other 16 teams have a record of Played 4, Won 0, Drawn 3, Lost 1.

There are various methods to determine which of the other four teams in the groups have come second, and these teams go forward to the quarter finals. The other twelve all leave the tournament having lost exactly one game.

In the quarter finals there are four team that have lost no games and four teams that have lost one game. The four group winners all lose to the four group runners up. Meaning the four group winners all leave the tournament having lost exactly one game, their quarter final.

At this point all 16 teams to leave the tournament have lost exactly one game

And there are four teams remaining that have lost one game.

The World Champion team will lose no further games, so they lose a total of one game. The losing finalist will lose one further game (the final), so they lose a total of two games. The third-placed team will lose one further game (the semi final), so they lose a total of Two games. And the fourth-placed team will lose two further games (the semi final and the play off), so they lose a total of three games.

This means that a total of 17 teams finish the tournament having lost exactly one game.

But there is a better solution in an hour by Thomas Cappleman, which you will not believe.

]]>In the quarter finals the top teams in each of the groups play a game against the second-placed team from another group.

The winners of the four quarter-final games progress to the semi finals, and the four losers play no further matches.

In the semi finals, the two winners progress to the final, with the winners of the final becoming World Champions; the two losers play a Third-Fourth play off.

The questions is, what is the largest number of teams that can finish the tournament having lost exactly one game?

Answer at 9.00 on Monday

]]>- 5 T on a F - 5 Toes on a Foot
- 1000 Y in a M - 1000 Years in a Millennium
- 3 S and YO - 3 Strikes and You're Out
- 7 W of the W - 7 Wonders of the World
- 15 is FB in RU - 15 in Full Back in Rugby Union
- 1812 O - 1812 Overture
- 7 B for 7 B - 7 Brides for 7 Brothers
- 21 S in a G - 21 Shillings in Guinea
- WI 64 - When I'm 64
- YSYS 3 BF - Yes Sir Yes Sir 3 Bags Full

]]>

- 5 T on a F
- 1000 Y in a M
- 3 S and YO
- 7 W of the W
- 15 is FB in RU
- 1812 O
- 7 B for 7 B
- 21 S in a G
- WI 64
- YSYS 3 BF

Answer at 9.00 on Monday

]]>

Occasionally she arrives late using flexi-time, and often has the lift to herself. On these occasions she travels to the 13th floor and then walks up the stairs.

When leaving work, at the normal time or not, she travels in the lift to the ground floor, and never walks at all.

She doesn't like walking, so why does she do so when arriving late?

The employee is very short, and can only reach up as far as the button for floor 13. When going up with other people they can press 15 on her behalf; when alone she presses 13 and then walks. Going down she can always reach 0 or G for the Ground Floor.

]]>Occasionally she arrives late using flexi-time, and often has the lift to herself. On these occasions she travels to the 13th floor and then walks up the stairs.

When leaving work, at the normal time or not, she travels in the lift to the ground floor, and never walks at all.

She doesn't like walking, so why does she do so when arriving late?

Answer at 9.00 on Monday

]]>There are five houses painted different colours, and a person of different nationality lives in each house. The five owners each drink a different beverage, play a different sport and own a different pet.

- The Briton lives in the red house
- The Swede keeps a dog
- The Dane drinks tea
- The green house is on the left of the white house
- The green house's owner drinks coffee
- The footballer owns a bird
- The yellow house's owner plays baseball
- The person in the middle house drinks milk
- The Norwegian lives in the first house
- The volleyball player lives next to the cat owner
- The horse owner lives next to the baseball player
- The tennis player drinks beer
- The German plays hockey
- The Norwegian lives next to the blue house
- The volleyball player's neighbour drinks water

Who owns the fish?

The best approach is to create a grid with house numbers across the top and Features (such as Pet or Nationality) down the side, and then use the facts to fill in the grid.

From Fact 9 the Norwegian lives in the leftmost house.

And from Fact 8 Milk is drunk in the middle house.

Then Fact 14 means that house two (next to the Norwegian) is Blue.

From Fact 5 we can see the Green house can't be house three as the owner doesn't drink milk. And from Fact 4 we can see it is on the left of another house that is White. The only place for the Green house is number 4, and house 5 is then white. Coffee is drunk in house 4.

From Fact 1 the Briton's Red house can't be number 1 (as that's inhabited by a Norwegian), so he must live in house number 3.

Yellow is now the only colour left for house number 1.

Then Fact 7 shows that the baseball player is in (the Yellow) house number 1.

And then Fact 11 gives the horse owner in house number 2, next to the baseball player.

Fact 12 informs us that the tennis player drinks beer. He can't be British (drinks Milk) or Norwegian (plays Baseball); Fact 3 shows he can't be Danish (drinks Tea) and Fact 13 shows he can't be German (plays Hockey). So he must be Swedish and from Fact 2 we know he keeps dogs.

This can fit in house number 5 only.

From Fact 3, the tea-drinking Dane can live in house number 2 only.

And the German must be in house number 4.

And we already know the German plays Hockey from Fact 13.

The only place for the water drinker is house number 1.

Fact 15 gives the Volleyball player in house number 2.

And then the footballer is in house number 3, and Fact 6 shows he owns birds.

Fact 10 gives the cat owner in house number 1.

And we have one space left for the Fish fancier to live in house number 4.

The fish is owned by the German.

]]>There are five houses painted different colours, and a person of different nationality lives in each house. The five owners each drink a different beverage, play a different sport and own a different pet.

- The Briton lives in the red house
- The Swede keeps a dog
- The Dane drinks tea
- The green house is on the left of the white house
- The green house's owner drinks coffee
- The footballer owns a bird
- The yellow house's owner plays baseball
- The person in the middle house drinks milk
- The Norwegian lives in the first house
- The volleyball player lives next to the cat owner
- The horse owner lives next to the baseball player
- The tennis player drinks beer
- The German plays hockey
- The Norwegian lives next to the blue house
- The volleyball player's neighbour drinks water

Who owns the fish?

Answer at 9.00 on Monday

]]>Both trains start simultaneously, heading towards each other at exactly 30 miles per hour. Startled by the train moving, the fly starts flying along the track towards the other train at exactly 40 miles per hour.

[Please note that these are special, theoretical "puzzle" trains and fly, and they will instantly start travelling at the stated speed, with no need for acceleration!]

After a while the fly reaches the other train, hits the front of it, bounces back and starts flying towards the first train at 40 miles per hour.

This process continues, with the fly traversing the ever-decreasing distance between the two trains, shuttling back and forth at 40 miles per hour.

Eventually the two trains collide, crushing the fly. And probably incurring other damage as well, but these are special, theoretical "puzzle" trains and no one, apart from the fly, is harmed.

What is the total distance covered by the fly, adding up all the ever-shortening flights between the trains?

The two trains are 60 miles apart, and as both travel at 30 miles per hour, the closing speed is 60 miles per hour. This means that it takes one hour for them to meet and crash into each other.

In one hour the fly, which is travelling at 40 miles per hour, will cover 40 miles.

The answer is 40 miles, with no need to try to calculate the sum of every decreasing distances!

]]>Both trains start simultaneously, heading towards each other at exactly 30 miles per hour. Startled by the train moving, the fly starts flying along the track towards the other train at exactly 40 miles per hour.

[Please note that these are special, theoretical "puzzle" trains and fly, and they will instantly start travelling at the stated speed, with no need for acceleration!]

After a while the fly reaches the other train, hits the front of it, bounces back and starts flying towards the first train at 40 miles per hour.

This process continues, with the fly traversing the ever-decreasing distance between the two trains, shuttling back and forth at 40 miles per hour.

Eventually the two trains collide, crushing the fly. And probably incurring other damage as well, but these are special, theoretical "puzzle" trains and no one, apart from the fly, is harmed.

What is the total distance covered by the fly, adding up all the ever-shortening flights between the trains?

Answer at 9.00 on Monday

]]>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?

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

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

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

]]>