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Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

Consecutive Numbers

Stage: 2 Challenge Level: Challenge Level:1

We had a very good set of solutions sent in from Bomere Heath Primary School. Here are a couple of examples but all of their contributions are well worth looking at here: BomereSchoolSolutions.doc or BomereSchoolSolutions.pdf

Shauna and Bethany:

First we found all the combinations for adding and subtracting four consecutive numbers. Then we found out the answer for them.
We did this two times then we looked for patterns such as:

1)+++ =2 middle numbers added together then x2.
2)--- =last number x2 in the negatives.
3)+-- =-4.
4)++- =first number times 2.
5)-++ =3rd number x2.
6)--+ =0.
7)-+- =-2.
8)+-+ = 2nd number x2.
9)= All even.
and that’s what we found out:)

From Archie and Jodie:

Firstly we wrote down four consecutive numbers, in our case 3, 4, 5, 6 then we found all the diffrent combinations eg: 3+4+5+6, 3-4-5-6, 3+4+5-6, 3+4-5-6
After that we found out all the answers for them.
Next we did the same process but with 22, 23, 24, 25 and found out all the combinations eg: 22+23-24+25, 22-23+24+25, 22-23-24+25, 22-23+24-25
Then we some patterns like with + + + if you add the two middle numbers together then double it you get the answer.
And with - + - the answer is always -2.
And with - - + the answer is always 0.
And with + - + you double the second number to get the answer.
And with + - - the answer is always -4.
And with - + + you double the third number to get the answer.
And with + + - you double the first number to get the answer.
And with - - - you double the end number to get the answer.
We hope you like our solution and hope it helps you if you do this challenge.

We had the following from St. Paul's Primary School:

Our answers are as follows;

In each answer we noticed that there are pairs of answers which belong together.
For example, 26 and -16, 12 and -2. The reason for this is that they have the same unit number.
We also noticed that the difference between these pairs is 10, except for the pair 26 and -16, which is 42.
All the positive answers are over 10.
If there are two subtractions signs the answer is a negative number.
If there are two add signs the answer will be a positive number.
All the answers are even.

Thank you for all the solutions that were sent in, it was really good to read about all the things you have found out. Keep up investigating Maths!