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Puzzle 525
In this puzzle, all of the numbers from 1 to 8 are used.
The differences (larger – smaller) between any two connected numbers are all different.
Can you complete the grid?
Note: this puzzle is not interactive, and cannot be clicked.
Hint
The largest possible difference is when 1 is next to 8, a difference of 7. Since we have 7 differences to find, and the largest possible difference is 7, all of the possible differences must exist. Start by looking where can the 8 go.
Answer
Reasoning
The largest possible difference is when 1 is next to 8, a difference of 7. Since we have 7 differences to find, and the largest possible difference is 7, all of the possible differences must exist: 1, 2, 3, 4, 5, 6, 7, and let's call these D1, …, D7.
D7 can only happen when: 1 is next to 8 = D7
D6 can happen when:
1 is next to 7, but these are given numbers that are not next to each other. 2 is next to 8 = D6
Where can 8 go? If we put 8 above 1, we cannot also satisfy D6 (2 is next to 8).
Therefore, we have two possibilities:
(a) 8 to the left of 1
(b) 8 to the right of 1 (a) 8 to the left of 1
By D6, 2 would be below 8, and this would give us D1, D6, D7. What can we place to the right of 1?
3 – no, because the difference between 1 and 3, and the difference between 3 and 5, are both D2.
4 – no, because the difference between 4 and 5 is D1, which we would already have.
6 – no, because the difference between 5 and 6 is D1, which we would already have.
There are no possible numbers we can place to the right of 1, so 8 can't go to the left of 1. (b) 8 to the right of 1
By D6, 2 would be above 8, and this would give us D3, D6, D7.
4 can't go next to 1, otherwise we'd create another D3. Therefore, 4 goes in the bottom left corner.
We are now left with 3 and 6.
If 6 went above 4, and 3 above 1, these would both be D2.
Therefore, 3 goes above 4, 6 goes above 1.
The final answer is:
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Puzzle 526
Imagine a bottle recycling skip, empty other than one lonely bottle.
Every hour, on the hour, people come and put bottles into the skip.
The first hour, at noon, one person came and put a bottle in.
One hour later, two people each placed a bottle into the skip.
An hour later, four people each placed a bottle into the skip.
This doubling of people continued until 11pm, when the skip was finally full.
Freddie was in love with three girls from his school! He couldn't decide which one he wanted to give his heart to so he sent all three a Valentine's card. But poor Freddie was out of luck, as each girl thought the card came from someone else and Freddie was left on the sideline.
From the clues below, can you work out the name of each potential sweetheart, the colour of each card Freddie sent and the name of the boy each girl believed the card was sent by?
Unluckily for Freddie, when Miss Jetson received her card, she thought it was from Adam. When Molly received her blue coloured card, she told Miss Hanson and together they worked out who the card was from. It didn't occur to either of them that it was from Freddie! The girl who received the red card was convinced it came from Ethan. Neither Millie nor Miss Motson received a pink card.
First Names: Lily, Millie, Molly
Surnames : Hanson, Jetson, Motson
Colours : Blue, pink, red
Boys : Adam, Dylan, Ethan
Hint
Start by using (2) and (4) to find who received the pink card.
Answer
Lily Jetson Pink Adam
Millie Hanson Red Ethan
Molly Motson Blue Dylan
Reasoning
By (2), Molly received the Blue card:
Lily
Millie
Molly Blue
We now know that Molly didn't receive the Pink card, and by (4), neither did Millie, which means that Lily received the Pink card (and Millie received the Red):
Lily Pink
Millie Red
Molly Blue
By (4), the two girls who didn't receive the Pink card are Millie and Miss Motson, and we already know that Millie and Molly didn't receive the Pink Card, which means that Molly is Miss Motson.
Lily Pink
Millie Red
Molly Motson Blue
By (3), the Red card was thought to have come from Ethan:
Lily Pink
Millie Red Ethan
Molly Motson Blue
By (1), Miss Jetson's card was thought to have come from Adam, this can't be Molly (Motson), nor Millie (Ethan). So it must be Lily Jetson:
Lily Jetson Pink Adam
Millie Red Ethan
Molly Motson Blue
The puzzle can now be completed:
Lily Jetson Pink Adam
Millie Hanson Red Ethan
Molly Motson Blue Dylan
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Puzzle 528
Can you find the book titles hidden in these phrases?
ROME OR OSLO? ANDREW, JULIE, TO VISIT. WARM TOO FEW, THE SUBWORLD SNEEZES AN I MALL? SHOPS, FAR MALLS? GO NEXT, GO! WITHOUT OTHER I DWINDLE. GO! WATER. SHIP, BOAT. STORM! DOWN RAIN! BRAVERY IN A NEW AGE, WORLD'S HOPE.
For each word in the title, new letters are added of the same length, and then the spacing is changed, and punctuation is added.
For example:
BOOK TITLE
BOOK 1234 TITLE 12345
BOOK NIGH TITLE APTUP
BOOKNIGHTITLEAPTUP
BOO, KNIGHT. IT LEAPT UP!
Answers
ROME OR OSLO? ANDREW, JULIE, TO VISIT.
ROMEO ROSLO AND REW JULIET OVISIT
= ROMEO AND JULIET
WARM TOO FEW, THE SUBWORLD SNEEZES
WAR MTO OF EW THE SUB WORLDS NEEZES
= WAR OF THE WORLDS
AN I MALL? SHOPS, FAR MALLS?
ANIMAL LSHOPS FARM ALLS
=ANIMAL FARM
GO NEXT, GO! WITHOUT OTHER I DWINDLE. GO!
GONE XTGO WITH OUTO THE RID WIND LEGO
= GONE WITH THE WIND
WATER. SHIP, BOAT. STORM! DOWN RAIN!
WATERSHIP BOATSTORM DOWN RAIN
= WATERSHIP DOWN
BRAVERY IN A NEW AGE, WORLD'S HOPE.
BRAVE RYINA NEW AGE WORLD SHOPE
= BRAVE NEW WORLD
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It is now three years since I first asked for support, and I would like to sincerely thank everyone who has helped me. BrainBashers doesn't show adverts, and I continue to depend on the ongoing support from everyone who enjoys the site.
