Ribbon Puzzle
I recently asked my friend Alex to buy me some ribbon for my child's bonnet.
Alex went to the haberdashery shop for the required length but accidentally swapped the feet and inches.
When I measured the resulting ribbon I only had 5÷8 of the length I required.
How much ribbon did I originally ask for?
Remember that there are 12 inches in each foot.
Solution (Previous Puzzle):
Remembering that:
E + E = E
O + O = E
E + O = O
To discuss individual letters it's easiest to represent the sum as:
A B C
D E F +
--------
G H I J
The largest values for A and D are 6 and 8, which makes G = 1.
Since column 2 is E + O = O there can be no carry from column 1 (since E + O + 1 is always even). Therefore C and F are 3 and 5 (but we don't yet know which is which), therefore J = 8.
There can't be a carry from column 2 (as A + D is even) therefore E can't be 9 as this would force a carry.
Therefore I = 9. Hence B can't be 0. Therefore H = 0.
The last remaining odd number makes E = 7. Making B = 2.
Therefore A and D are 4 and 6 (but we don't yet know which is which).
Since the top row's digits have to add to 9 the top number must be 423.
This makes the sum 423 + 675 = 1098.
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