Answer
The letter was written on a typewriter which has a problem with the middle row of letters, which print spaces instead. The letter should have read:
Dear Sir,
I recently visited one of your outlets to buy one of your typewriters. However, as you can see I am having a small problem.
The middle row of the keyboard appears to be faulty.
I would be very grateful if you could despatch a replacement by return post. Failing this, could you please send an engineer to resolve this problem as a matter of urgency.
Yours faithfully,
Mrs Middins.
???
Puzzle 6
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:
?
Puzzle 7
Starting in the bottom left corner and moving either up or right, adding up the numbers along the way, what is the largest sum that can be made?
2
3
5
4
1
3
2
4
3
4
5
1
3
5
2
3
3
2
3
1
1
4
2
4
4
Note: this puzzle is not interactive, and the numbers cannot be clicked.
