Doras, Maxine & Ella’s Solution
For the first one, we wrote a 3 times tables chart
down from 0-9 because it has to be 1 digit number. We noticed that the numbers 1 to 9 only appeared once in the answers. Then we looked back at the question and saw that 3 x 'e' had to be 3 x 7 because it had the only 1 at the end and this
meant that the 'e' at the bottom had to be 7 too. Because the 2 in 21
had to go up we subtracted 2 by 7 which is 5. At this stage we knew that
the letter 'd' had to end in 5. So 3 x 'd' had to be 3 x 5 since it is the only
one that ends in 5 and this meant that the d at the bottom had to be 5 too.
Now because the 1 was at the top the 5 is at the bottom, 5 subtracts 1 so it
is 4 the only one that ends in 4 is 3 x 8 which is 24 so 'c' is 8. The 'c' at the
bottom will also be 8.The 2 should be up there so 8-2 is 6 and 3 x 2 is 6 so
'b' should be 2. This means that there is no numbers that you will have to
carry up. So it is 2 at the end and 4 x 3 is 12 so 'a' is 4 and we carry the 1.
Finally my solution was 142857 x 3 = 428571.
We think that there is only one solution to this problem.
Here is the solutions explained in another way: e x 3=*1=7 x 3=21
d x 3+2=*7=7-2=5
=d x 3= *5=5 x 3=15
c x 3+1=*5=5-1=4
c x 3=*4=8 x 3=24
24+1=25
b x 3+2=*8=8-2=6
b x 3=6=2 x 3=6
6+2=8
a x 3=*2=4 x 3=12
We used the same method for the 2nd problem. And the answer is:
285714x3=857142.