Consider the numbers of toys made. There are five whole numbers, all greater than 2, all different, which add up to 30. They contain a run of three consecutive ones, and a pair of which one is triple the other. The pair must be (3,9) or (4,12), because if it were (5,15), you would have the other three numbers adding to 10, but the smallest available numbers are 3, 4, and 6, whose sum is 13.
If the pair is (3,9), the run cannot be (7,8,9), because the last number would have to be another 3. The run cannot be (3,4,5), because the last number would have to be another 9; so the run has to be (5,6,7), and the numbers are (3,5,6,7,9). Furthermore, the green elf made 3, the red elf made 5, Cher made 6, 7 sleds were made, and Sue made 9 tops.
If the pair is (4,12), the run cannot be (10,11,12), because the sum is already 37 > 30. The run cannot be (4,5,6), because then the 4 toys would be made by an elf dressed in both red and green, which is impossible. Thus the run must be (3,4,5), and the last number is 6. That makes the numbers (3,4,5,6,12). Furthermore the red elf made 3, Cher wore green and made 4, 5 sleds were made, and Sue made 12 tops.
In either case, Sue made the tops.
In the second case,
we can establish that neither Cher, Johnny, Jane, Sue, nor Marcia can
be wearing yellow. That is because Cher is wearing green, Johnny made
racing cars (and the yellow elf made trains), Jane made sleds, Sue made
tops, and Marcia wears orange. This is a
In the first case, you do get a solution. At this point you know:
Cher does not wear red or orange or green, does not make sleds, cars, or tops, and makes 6 toys.
Johnny does not wear red or yellow or orange, makes cars, and doesn't make 5, 6, 7, or 9 toys.
Jane wears red, doesn't make sleds, cars, trains, or tops, and makes 5 toys.
Sue doesn't wear red, yellow, green, or orange, makes tops, and makes 9 toys.
Marcia wears orange, doesn't make cars, trains, or tops, and doesn't make 3, 5, 6, or 9 toys.
Now by a process
of elimination, you can determine how many toys Marcia and Johnny make,
which toy Jane makes, and what color Sue wears, who makes sleds, who
makes trains, who makes 3 toys, who makes 7 toys, what the red elf makes,
how many toys the yellow elf makes, how many toys the orange elf makes,
how many cars are made, what color the elf who
Now everything else is determined uniquely.
to the Problem
The Little Red Schoolhouse