Below you can find 8 words that have had their beginnings and endings removed. In each case, the same two letters can be found at the beginning and the end. For example REspiRE. --qui----yli----tat----gib----liv----rmi----ifi----alg--
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 7
What four-letter word can be placed between the two following words to make two new words:
table[----]house
In the following example, the word 'book' creates the words 'cookbook' and 'bookcase'.
cook[book]case
Workers with the surnames Baker, Teacher, Carpenter, and Plumber are currently attending an annual convention.
No-one is currently, nor has ever been, in the same occupation as their name, and no-one has had the same occupation twice. Charlie has never been a carpenter, and Mr Teacher is now a plumber. Davie used to be a teacher, but Mr Billie Baker never has. Mr Plumber is not called Eddie, and Mr Carpenter wasn't previously a teacher. The previous occupations were all different, and the current occupations are all different.
Can you determine the full names of each of the attendees, along with their current and previous occupation?
The previous occupation is followed by the current.
Reasoning
The four forenames are: Billie, Charlie, Davie, Eddie.
The four surnames are: Baker, Teacher, Carpenter, Plumber
The four occupations are: baker, teacher, carpenter, plumber.
By (3), we have Billie Baker:
Billie Baker – ? + ?
Teacher – ? + ?
Carpenter – ? + ?
Plumber – ? + ?
By (2), Mr Teacher is currently a plumber:
Billie Baker – ? + ?
Teacher – ? + plumber
Carpenter – ? + ?
Plumber – ? + ?
By (3) Mr Baker was not previously a teacher. By (4), neither was Mr Carpenter. And by (1) Mr Teacher can't have been either. Therefore, Mr Plumber used to be a teacher, and is called Davie:
Billie Baker – ? + ?
Teacher – ? + plumber
Carpenter – ? + ?
Davie Plumber – teacher + ?
By (3), Mr Baker has never been a teacher, and by (1), Mr Plumber can't currently be a teacher either. Also, by (1), neither can Mr Teacher. Therefore, Mr Carpenter must currently be a teacher:
Billie Baker – ? + ?
Teacher – ? + plumber
Carpenter – ? + teacher
Davie Plumber – teacher + ?
By (1), Mr Baker can't be a baker, so only Mr Plumber can currently be a baker. Leaving Mr Baker as a carpenter currently:
Billie Baker – ? + carpenter
Teacher – ? + plumber
Carpenter – ? + teacher
Davie Plumber – teacher + baker
By (1), only Mr Teacher could have previously been a carpenter:
Billie Baker – ? + carpenter
Teacher – carpenter + plumber
Carpenter – ? + teacher
Davie Plumber – teacher + baker
By (2), Charlie has never been a carpenter, and since Mr Teacher has, Charlie must be Mr Carpenter.
Billie Baker – ? + carpenter
Teacher – carpenter + plumber
Charlie Carpenter – ? + teacher
Davie Plumber – teacher + baker
By (1), we now know all of the occupations, and Eddie must be Mr Teacher:
Billie Baker – plumber + carpenter
Eddie Teacher – carpenter + plumber
Charlie Carpenter – baker + teacher
Davie Plumber – teacher + baker
