Well done to all of you who gave a
correct solution to this problem. The correct answer to the first
part of the question is 33, 48, 38
There are several correct answers to
the second part of the problem including:
Richard from Burlingame school used a
systematic approach to help him find the answer to the second
part of the problem:
What I did was muliply each number by 2, then 3, then 4, etc till
I found a pattern. If you muliply the number by 6, you come out
with a number 10 less than the answer. I simply added ten, then
subtracted 0 to give me the answer.
Quite a few of you used a really useful technique to help find
the solution more efficiently including Marley and Jake from
Swarcliffe Primary and Shiv from Mayplace Primary School. Ester
age 8 sent in a nice solution:
The numbers are CONSECUTIVE going in and HAVE A DIFFERENCE OF 6
coming out. This tells us that there must be a multiplication by
6 somewhere.
She also spotted that there was more than
one solution:
If x6 is in the middle circle some solutions could be +2, x6, -2
+1, x6, +4 -1, x6, +16 If you multiply by six first you have to
add or subtract in the last two cicles so that the result is +10
x6,+6,+4 x6,+11,-1 You cannot make the x6 the last thing you do
because the numbers coming out are not in the six times table.
As you can see, there are lots of possible solutions using
multiply by 6 as one of the functions, but you can also split
multiply by 6 into multiply by 3 and multiply by 2, or as several
pupils from the Mount School in York observed, multiply by 12 and
divide by 2.