The initial letters from the nursery rhyme, Hickory Dickory Dock.
Hickory, dickory, dock,
The mouse ran up the clock,
The clock struck one,
The mouse ran down,
Hickory, dickory, dock.
Answer
I asked for 9 foot 2 inches (110 inches) and my friend brought me 2 foot 9 inches (33 inches).
Reasoning
I asked my friend to buy me A feet and B inches, which is a total of 12A + B inches.
He accidentally bought me B feet and A inches, which is 12B + A inches.
We know that 12B + A is actually only 30% of what I wanted, so:
12B + A = 0.3 x (12A + B)
Multiply throughout by 10:
120B + 10A = 3 x (12A + B)
120B + 10A = 36A + 3B
117B = 26A
B = 26A ÷ 117
Don't forget that A and B can only be integers, and between 0 and 11.
Since 26 x A has to be at least 117, the lowest possible value for A is 5. We can check the remaining possibilities.
5 x 26 = 130
6 x 26 = 156
7 x 26 = 182
8 x 26 = 208
9 x 26 = 234 (*)
10 x 26 = 260
11 x 26 = 286
The only number wholly divisible by 117 is 234, which means that A = 9, and B = 2.
