How do you solve abacus 6 challenge master 8?

Answer 1

Abacus 6 challenge master 8 looks at consecutive addition.

(After my husband and 10 year old daughter struggled with this all day - I thought the following might be useful to other parents also struggling. It is not definitive (I am not a Maths graduate), but it works.)

A very useful table can be produced (Jackson's Table) - preferably with the help of Excel or similar. The first few lines are produced below.

No. 2 3 4 5 6 (consecutive numbers)

1 3 6 10 15 21

2 5 9 14 20 27

3 7 12 18 25 33

.

.

n 2n+1 3n 4n+6 5n+10 6n+15

The numbers set in the problem can all then be found; hence 9 appears twice and 75 appears 4 times.

The observations to be drawn are that:

1. all odd numbers can be made from 2 consecutive numbers, but that even numbers cannot.
2. Any number divisible by 3 (except 3 itself) can be made by adding 3 consecutive numbers
3. Any 5 consecutive numbers added together will always give a multiple of 5
4. Multiples of 4 cannot be made by adding consecutive numbers unless that multiple is also a multiple of 3 or 5