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 we place the 8? 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?
Not 3, because the difference between 1 and 3, and the difference between 3 and 5, are both D2.
Not 4, because the difference between 4 and 5 is D1, which we would already have.
Not 6, 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 18
Below are five phrases that have been altered. Rearrange the words so that when they are read aloud they will sound very similar to the required phrase. For example "Ducks Sits Hound Fa Mill Ear" = "Does it sound familiar".
crows dose my off wind
cab chalk clicks fizz lie lye ox soft
a crowed fall jest lobe Rick oath yell
beef four heap luck Yule
dud rough wharf whorls
Answer
my crows off wind dose = Microsoft Windows
lie fizz lye cab ox soft chalk clicks = Life is like a box of chocolates
jest fall oath a yell lobe Rick crowed = Just follow the yellow brick road
luck beef four Yule heap = Look before you leap
wharf rough dud whorls = War of the Worlds
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Puzzle 19
Combine the word fragments below to produce pairs of words that have opposite meanings. There are 9 pairs of words, one pair on each line.
For example, USE REF EPT ACC becomes ACCEPT + REFUSE.
AB ANT RCE SCA UND
