1, 14 + 15 + 16 + 17 = 62
2, 14 - 15 - 16 - 17 = -4
3, 14 + 15 - 16 + 17 = 30
4, 14 - 15 + 16 - 17 = -2
5, 14 + 15 + 16 - 17 = 28
6, 14 - 15 - 16 + 17 = 0
7, 14 + 15 - 16 - 17 = -4
8, 14 - 15 + 16 + 17 = 32
The numbers are all even
Numbers 20, 21, 22, 23:
1, 20 + 21 + 22 + 23 = 86
2, 20 - 21 - 22 - 23 = -46
3, 20 + 21 - 22 + 23 = 42
4, 20 - 21 + 22 - 23 = -2
5, 20 + 21 + 22 - 23 = 40
6, 20 - 21 - 22 + 23 = 0
7, 20 + 21 - 22 - 23 = -4
8, 20 - 21 + 22 + 23 = 44
Compare the sets:
The numbers are all even in both sets. The sets of numbers
both have 3 negative numbers and 5 other numbers - one of which is
0! Both of them include -2 in them.
Test
This is a test to see
whether each pattern contains 3 negative numbers one 0, and 4 other
numbers.
Numbers 54, 55, 56,
57:
1, 54 + 55 + 56 + 57
= 222
2, 54 - 55 - 56 - 57 = -144
3, 54 + 55 - 56 + 57 = 110
4, 54 - 55 + 56 - 57 = -2
5, 54 + 55 + 56 - 57 = 108
6, 54 - 55 - 56 + 57 = 0
7, 54 + 55 - 56 - 57 = -4
8, 54 - 55 + 56 + 57 = 112
Test complete.
New Rule
- Consecutive Numbers backwards
Numbers 63, 62, 61, 60:
1, 63 + 62 + 61 + 60 = 246
2, 63 - 62 - 61 - 60 = 120
3, 63 + 62 - 61 + 60 = 124
4, 63 - 62 + 61 - 60 = 2
5, 63 + 62 + 61 - 60 = 126
6, 63 - 62 - 61 + 60 = 0
7, 63 + 62 - 61 - 60 = 4
8, 63 - 62 + 61 + 60 = 122
Here, there are no negative numbers - -4
became 4 and -2 became 2 !
Numbers 04, 03, 02, 01:
1, 4 + 3 + 2 + 1 = 10
2, 4 - 3 - 2 - 1 = -2
3, 4 + 3 - 2 + 1 = 6
4, 4 - 3 + 2 - 1 = 2
5, 4 + 3 + 2 - 1 = 8
6, 4 - 3 - 2 + 1 = 0
7, 4 + 3 - 2 - 1 = 4
8, 4 - 3 + 2 + 1 = 4
There is one negative number again -2, -4
has changed to two +4 [not a sum].
Comparing [with the other rule]: Answer 6
stays as 0. The negative numbers have become positive, [normal]
numbers [i.e. -2 = 2 -4 = 4 ] This is because you take lower
numbers, and add higher numbers.
Pupils from William
Harding Combined School and also from Gorseland Primary School
investigated these consecutive numbers as well. They tried many
different sets of four consecutive numbers and all agreed with what
Stuart (from William Harding) wrote:
I found out that there are 8 sums for every set of consecutive
numbers 1 full add,1 full subtract, 3 with 2 adds and 3 with 2
subtracts.
The group from Gorseland also found three
rules (if the numbers are in ascending order):