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The Answers

Challenge ‘14

Danegeld

Egil and Kol have both returned home with Danegeld given to them to buy off their invasions of Anglo Saxon England. Together, they received 25,000 pieces of silver; however, Egil had 7,000 more than Kol. How much silver did each of them take back?

Valhalla at Ragnorak

Odin’s great hall of Valhalla has many doors. For every Oak door, there are 4 Elm doors. For every Elm door, there are 3 Pine doors. There is a Larch door to the left of every Oak and every Elm door, and an Ash door to the right of every Oak and every Elm door. 800 warriors will march out through each door at the start of Ragnorak. There are 20 Oak doors. How many warriors will there be?

Valhalla at Ragnorak

There are 20 Oak doors

For every Oak door, there are 4 Elm doors.

For every Elm door, there are 3 Pine doors.

There is a Larch door to the left of every Oak and every Elm door, and an Ash door to the right of every Oak and every Elm door.

Valhalla at Ragnorak

540 doors => 800 × 540 = 432,000 warriors

Loki, the trickster god, offers to give you the treasure in a chest if you can crack the five-digit combination. He gives you 5 clues: Each digit is 0, 1, 2, 3, 4 or 5; no digit is repeated; the first digit is an even number; the first three digits add up to 4; the fifth digit is larger than the fourth. He will allow you 6 attempts to open the lock. Can you guarantee successfully opening the lock?

Loki’s gameLoki’s game a chest if you can crack the five-digit combination. He gives you 5 clues: Each digit is 0, 1, 2, 3, 4 or 5; no digit is repeated; the first digit is an even number; the first three digits add up to 4; the fifth digit is larger than the fourth. He will allow you 6 attempts to open the lock. Can you guarantee successfully opening the lock?

First digit is 0, 2 or 4

First 3 must be 0,1,3 or 0,3,1

Fourth and fifth must be 2,4 or 4,5 or 2,5

Each digit is 0, 1, 2, 3, 4 or 5;

no digit is repeated;

the first digit is an even number;

the first three digits add up to 4;

the fifth digit is larger than the fourth

Loki’s game a chest if you can crack the five-digit combination. He gives you 5 clues: Each digit is 0, 1, 2, 3, 4 or 5; no digit is repeated; the first digit is an even number; the first three digits add up to 4; the fifth digit is larger than the fourth. He will allow you 6 attempts to open the lock. Can you guarantee successfully opening the lock?

2

1

3

1

1

0

5

4

1

1

1

1

1

0

5

4

1

2

1

1

3

2

2

1

0

1

1

0

3

2

1

1

1

1

0

5

1

2

1

0

1

1

1

1

1

0

5

3

2

1

1

2

0

1

2

3

1

1

1

1

5

0

1

1

2

4

3

0

1

1

1

1

0

1

5

3

2

1

3

1

2

4

0

1

Not Fork Handles! a chest if you can crack the five-digit combination. He gives you 5 clues: Each digit is 0, 1, 2, 3, 4 or 5; no digit is repeated; the first digit is an even number; the first three digits add up to 4; the fifth digit is larger than the fourth. He will allow you 6 attempts to open the lock. Can you guarantee successfully opening the lock?

Idunn collects candle stumps from around Asgard. She can make a new candle from 4 stumps. A candle will provide light for one night, whilst burning down to a stump. She collects 64 candle stumps. For how many nights will she have light, starting with these 64 stumps?

Not Fork Handles! a chest if you can crack the five-digit combination. He gives you 5 clues: Each digit is 0, 1, 2, 3, 4 or 5; no digit is repeated; the first digit is an even number; the first three digits add up to 4; the fifth digit is larger than the fourth. He will allow you 6 attempts to open the lock. Can you guarantee successfully opening the lock?

Not Fork Handles! a chest if you can crack the five-digit combination. He gives you 5 clues: Each digit is 0, 1, 2, 3, 4 or 5; no digit is repeated; the first digit is an even number; the first three digits add up to 4; the fifth digit is larger than the fourth. He will allow you 6 attempts to open the lock. Can you guarantee successfully opening the lock?

21 nights

A barrel of laughs a chest if you can crack the five-digit combination. He gives you 5 clues: Each digit is 0, 1, 2, 3, 4 or 5; no digit is repeated; the first digit is an even number; the first three digits add up to 4; the fifth digit is larger than the fourth. He will allow you 6 attempts to open the lock. Can you guarantee successfully opening the lock?

Adric’s barrel contains 24 pints of Viking Mead, which are to be shared equally between Adric, Beowolf and Canute. Unfortunately there are only 3 containers available: Doris the barmaid’s bowl of capacity 5 pints, Beowolf’s jug of capacity 11 pints, and Canute’s bucket of capacity 13 pints. If each man is going to take his share in his container, how should the containers be used to give each man his fair share?

(It is not possible to pour beer back into the barrel, and Doris must get her bowl back before the three men leave).

A barrel of laughs a chest if you can crack the five-digit combination. He gives you 5 clues: Each digit is 0, 1, 2, 3, 4 or 5; no digit is repeated; the first digit is an even number; the first three digits add up to 4; the fifth digit is larger than the fourth. He will allow you 6 attempts to open the lock. Can you guarantee successfully opening the lock?

Adric

Beowolf

Canute

Doris

24

8

13

3

0

8

11

8

13

5

0

5

0

Dig This a chest if you can crack the five-digit combination. He gives you 5 clues: Each digit is 0, 1, 2, 3, 4 or 5; no digit is repeated; the first digit is an even number; the first three digits add up to 4; the fifth digit is larger than the fourth. He will allow you 6 attempts to open the lock. Can you guarantee successfully opening the lock?

- Statue

- Stone Cross

Mervin has successfully hidden the treasure, but has forgotten where; all he can remember is the following clues:

The treasure is buried at the same distance from the stone cross and the old Oak Tree. It is also twice as far from the statue as it is from the cliff edge. Make an exact copy of the map, marking the centres of the cross, statue and tree, and the cliff edge, and mark with a X where the treasure is buried.

- Oak
- Tree

Cliff

Dig This a chest if you can crack the five-digit combination. He gives you 5 clues: Each digit is 0, 1, 2, 3, 4 or 5; no digit is repeated; the first digit is an even number; the first three digits add up to 4; the fifth digit is larger than the fourth. He will allow you 6 attempts to open the lock. Can you guarantee successfully opening the lock?

- Statue

- Stone Cross

- Oak Tree

Cliff

One L of a Field a chest if you can crack the five-digit combination. He gives you 5 clues: Each digit is 0, 1, 2, 3, 4 or 5; no digit is repeated; the first digit is an even number; the first three digits add up to 4; the fifth digit is larger than the fourth. He will allow you 6 attempts to open the lock. Can you guarantee successfully opening the lock?

Harald, when not with his raiding party in the North of England, tends his farm in Norway. His best field is an L-shape; you may think of this as a larger rectangle with a smaller rectangle cut from it.

The length of the larger rectangle is 2 metres longer than the width. The smaller rectangle has one side that is 8m shorter, and another side that is 6m shorter, than the width of the larger rectangle. The field has an area of 272m2 and he intends to fence it off with rope to keep in his cows.

Starting from one corner, he puts fenceposts at 3-metre intervals, but additional posts are then erected where they are required for keeping the rope taut.

How many fenceposts are needed?

One L of a Field a chest if you can crack the five-digit combination. He gives you 5 clues: Each digit is 0, 1, 2, 3, 4 or 5; no digit is repeated; the first digit is an even number; the first three digits add up to 4; the fifth digit is larger than the fourth. He will allow you 6 attempts to open the lock. Can you guarantee successfully opening the lock?

- Firstly, we need to establish the dimensions of the field.

w + 2

w

w - 6

w - 8

One L of a Field a chest if you can crack the five-digit combination. He gives you 5 clues: Each digit is 0, 1, 2, 3, 4 or 5; no digit is repeated; the first digit is an even number; the first three digits add up to 4; the fifth digit is larger than the fourth. He will allow you 6 attempts to open the lock. Can you guarantee successfully opening the lock?

So the dimensions of the larger rectangle are 20m by 22m, and the smaller rectangle is 12m by 14m. However…

One L of a Field a chest if you can crack the five-digit combination. He gives you 5 clues: Each digit is 0, 1, 2, 3, 4 or 5; no digit is repeated; the first digit is an even number; the first three digits add up to 4; the fifth digit is larger than the fourth. He will allow you 6 attempts to open the lock. Can you guarantee successfully opening the lock?

- There are 2 possible fields:

22m

22m

6m

8m

12m

14m

20m

20m

14m

12m

8m

10m

One L of a Field a chest if you can crack the five-digit combination. He gives you 5 clues: Each digit is 0, 1, 2, 3, 4 or 5; no digit is repeated; the first digit is an even number; the first three digits add up to 4; the fifth digit is larger than the fourth. He will allow you 6 attempts to open the lock. Can you guarantee successfully opening the lock?

Starting in this corner gives us 28 posts (this will always be the case)

We also need 4 extra posts.

In fact wherever we start, we get 32 posts.

22m

8m

14m

20m

12m

8m

One L of a Field a chest if you can crack the five-digit combination. He gives you 5 clues: Each digit is 0, 1, 2, 3, 4 or 5; no digit is repeated; the first digit is an even number; the first three digits add up to 4; the fifth digit is larger than the fourth. He will allow you 6 attempts to open the lock. Can you guarantee successfully opening the lock?

Again, starting here gives us 28 +4 = 32 posts.

However, if we start here, we only need 28 + 2 = 30 posts

The difference here is the two consecutive sides which are divisible by 3.

22m

6m

12m

20m

14m

10m

Rune Code a chest if you can crack the five-digit combination. He gives you 5 clues: Each digit is 0, 1, 2, 3, 4 or 5; no digit is repeated; the first digit is an even number; the first three digits add up to 4; the fifth digit is larger than the fourth. He will allow you 6 attempts to open the lock. Can you guarantee successfully opening the lock?

This letter is written in normal modern English. Your task is to decode it.

dear father brown,

it was terrible , the xiking warriors attacked the monastery at dawn.

they haxe plundered our treasure room and haxe made off with all of our gold and money.

they burnt down three barns and scared away all of the cows and pigs.

please send us any spare hens and geese you haxe.

yours,

brother matthew

Rune Code a chest if you can crack the five-digit combination. He gives you 5 clues: Each digit is 0, 1, 2, 3, 4 or 5; no digit is repeated; the first digit is an even number; the first three digits add up to 4; the fifth digit is larger than the fourth. He will allow you 6 attempts to open the lock. Can you guarantee successfully opening the lock?

dear father brown,

it was terrible , the xiking warriors attacked the monastery at dawn.

they haxe plundered our treasure room and haxe made off with all of our gold and money.

they burnt down three barns and scared away all of the cows and pigs.

please send us any spare hens and geese you haxe.

yours,

brother matthew

Rune Code a chest if you can crack the five-digit combination. He gives you 5 clues: Each digit is 0, 1, 2, 3, 4 or 5; no digit is repeated; the first digit is an even number; the first three digits add up to 4; the fifth digit is larger than the fourth. He will allow you 6 attempts to open the lock. Can you guarantee successfully opening the lock?

dear father brown,

it was terrible , thexiking warriorsattacked the monasteryat dawn.

theyhaxe plunderedour treasureroom andhaxe madeoff with all of our goldand money.

they burnt down three barnsandscaredawayall of the cowsand pigs.

pleasesendusanyspare hensand geeseyouhaxe.

yours,

brothermatthew

Rune Code a chest if you can crack the five-digit combination. He gives you 5 clues: Each digit is 0, 1, 2, 3, 4 or 5; no digit is repeated; the first digit is an even number; the first three digits add up to 4; the fifth digit is larger than the fourth. He will allow you 6 attempts to open the lock. Can you guarantee successfully opening the lock?

dear father brown,

it wasterrible , thexiking warriorsattackedthe monasteryatdawn.

they haxe plunderedourtreasureroom and haxe madeoff withall of our goldand money.

they burntdownthree barnsandscaredawayall of the cowsand pigs.

pleasesend us any sparehens and geeseyouhaxe.

yours,

brothermatthew

Rune Code a chest if you can crack the five-digit combination. He gives you 5 clues: Each digit is 0, 1, 2, 3, 4 or 5; no digit is repeated; the first digit is an even number; the first three digits add up to 4; the fifth digit is larger than the fourth. He will allow you 6 attempts to open the lock. Can you guarantee successfully opening the lock?

dearfatherbrown,

itwasterrible , thexikingwarriorsattackedthemonasteryatdawn.

they haxe plunderedourtreasureroomand haxemade offwithall ofour goldandmoney.

theyburntdownthreebarnsandscaredawayall ofthe cowsand pigs.

pleasesend us any sparehens and geeseyouhaxe.

yours,

brother matthew

Rune Code a chest if you can crack the five-digit combination. He gives you 5 clues: Each digit is 0, 1, 2, 3, 4 or 5; no digit is repeated; the first digit is an even number; the first three digits add up to 4; the fifth digit is larger than the fourth. He will allow you 6 attempts to open the lock. Can you guarantee successfully opening the lock?

dearfatherbrown,

itwasterrible , thevikingwarriorsattackedthemonasteryatdawn.

they haveplunderedourtreasureroomand havemade offwith all ofour goldandmoney.

theyburntdownthreebarnsandscaredawayallofthe cowsand pigs.

pleasesend us any sparehens and geeseyouhave.

yours,

brother matthew

Rune Code a chest if you can crack the five-digit combination. He gives you 5 clues: Each digit is 0, 1, 2, 3, 4 or 5; no digit is repeated; the first digit is an even number; the first three digits add up to 4; the fifth digit is larger than the fourth. He will allow you 6 attempts to open the lock. Can you guarantee successfully opening the lock?

dearfatherbrown,

itwasterrible , thevikingwarriorsattackedthemonasteryatdawn.

they haveplunderedourtreasureroomand havemade offwith all ofourgoldandmoney.

theyburntdownthreebarnsandscaredawayallofthecowsandpigs.

pleasesend us any sparehens and geeseyouhave.

yours,

brother matthew

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