Answers
cam – scam + camped
car – scar + carped
hip – ship + hipped
hop – shop + hopped
kip – skip + kipped
lap – slap + lapped
lip – slip + lipped
lop – slop + lopped
nap – snap + napped
nip – snip + nipped
tar – star + tarped
top – stop + topped
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Puzzle 818
Start from the central 'F' and move horizontally or vertically, and collect the letters needed to spell 'FIND' (in any order). How many routes can you take?
D
N
I
D
D
N
D
I
D
D
I
N
F
I
I
N
I
N
D
D
I
D
I
D
N
Note: this puzzle is not interactive, and the letters cannot be clicked.
Answer
There were 17 children, with 11 sweets each.
Reasoning
If we number the clues: each child had more than one sweetthere were more children than there were sweets per child
187 only has the factors 1, 11, 17, 187. Therefore, the only possible answers are:
1 child, with 187 sweets each – not allowed by (2)
11 children, with 17 sweets each – not allowed by (2)
17 children, with 11 sweets each (*)
187 children, with 1 sweet each – not allowed by (1)
Only one possible answer (*) isn't eliminated.
???
Puzzle 820
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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