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 3
Starting with COLD, change one letter at a time until you have the word WARM.
Each change leaves the other letters in their original places and must result in a common word.
What is the minimum number of steps required to achieve this change?
Answer
I asked for 7 feet, 4 inches and Alex brought me 4 feet, 7 inches.
Reasoning
If we label what I asked for as A feet and B inches, which is (12 x A + B) inches, then I actually received B feet and A inches, which is (12 x B + A) inches. Which means that:
5/8 x (12 x A + B) = (12 x B + A)
Simplifying gives:
A = 91/52 x B
As B is the number of inches, it can only be between 1 and 12 and must give A as a whole number of feet.
B = 4 is the only possible value, which means that A = 7.
So I originally asked for 7 feet, 4 inches.
Double-Checking
I received 4 feet, 7 inches = 55 inches.
I asked for 7 feet, 4 inches = 88 inches, and 88 x 5/8 = 55.
