Using all of the letters A to Z, each once only, complete these common words. There are currently 2 different answers, can you find them both? -ai-es-ua--e-el-o-ed-na-efog--c--mpb--jo-r-it-re-t-av-nmu--cmou--
Hint
The answer is 4 digits long, so what must G equal?
Answer
423 + 675 = 1098.
Reasoning
Remembering that:
even + even = even
odd + odd = even
even + odd = odd
To discuss individual letters, it's easiest to represent the sum as:
A B C
D E F +
————————
G H I J
A + D has to be over 9, which means that G = 1.
B + E = I, is even + odd = odd, which means that we can't have a carry from C + F (otherwise it would have been even + odd + 1, which is even).
The 1 has already gone, so the smallest possible value for either C or F is 3, which means that the other can't be 7 or 9 (otherwise we'd have a carry).
Therefore, C and F are 3 and 5, but we don't know which is which. But we do now know that J = 8.
A + D = H, is even + even = even, which means that we can't have a carry from B + E. Therefore, E can't be 9, as this would force a carry. So E = 7.
I is the only remaining odd number, so I = 9.
Which means that B = 2.
Neither A nor D can be 0 (otherwise we would have two of the same digit). So, H = 0.
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, A can't be 6, so A = 4, making C = 3.
This makes the sum 423 + 675 = 1098.
??
Puzzle 3
Starting with SOFT, change one letter at a time until you have the word LENS.
Each change leaves the other letters in their original places and must result in a proper word.
What is the minimum number of steps required to achieve this change?
SOFT
....
....
....
LENS
My 9, 6, 1, 2 is something a swimmer might do.
My 5, 4, 4, 3 is not that hot really.
My 7, 4, 3, 2 is a long piece of wood.
My 7, 6, 8, 5, 10 is a small part of something.
My 3, 4, 1, 10 is a deep affection.
My 7, 6, 8 is something you can eat.
My whole is an old form of transport.
