Sums of the Unexpected
The number 15 can be written as the sum of consecutive whole numbers in three ways.
15 = 7 + 8
15= 4 + 5 + 6
15= 1 + 2 + 3 + 4 +5
In how many ways can you write 105 as the sum of consecutive whole numbers?
In how many ways can you write 24 as the sum of consecutive whole numbers?
(A consecutive whole number is a number that comes directly after another whole number in a sequence, e.g. 5,6,7,8,9…)
Answer
There are 7 ways to represent 105 as a sum of consecutive numbers.
- 105 = 52+53
- 105 = 34+35+36
- 105 = 19+20+21+22+23
- 105 = 15+16+17+18+19+20
- 105 = 12+13+14+15+16+17+18
- 105 = 6+7+8+9+10+11+12+13+14+15
- 105 = 1+2+3+4+5+6+7+8+9+10+11+12+13+14
There is only one way to represent 24 as a sum of consecutive numbers.
- 24 = 7+8+9
How can you determine that you have found all the possible solutions?
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