# Making Maths Count

## Maths Week Scotland 2019 – Sums

October 2, 2019 by 3 Comments | Category Education, Games, Maths

Puzzle 3: Sums (almost) without Adding

If the first ten positive whole numbers are added, the sum is 55. Check it for yourself!

Use this information to find quick ways to sum the:

a)  whole numbers from 11 to 20

b)  first ten even numbers

c)  first ten odd numbers

d)  first twenty whole numbers

e)  first twenty multiples of 3

Solutions to Puzzle 3:

Answers a) 155  b) 110  c) 100  d) 210  e) 630

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• SMacD says:

11-20 = 155 not 165 as James O’Reilly says

• Sonia MacD says:

a) if 1-10 = 55
Then 11-20 = 55 + 10×10 = 155

b) if 1-10 = 55 then 2-20 = 55 x 2 = 110

c) if 1-10 = 55 then 1-19 = 55 x 2 – 10 = 100

d) if 1-10 = 55 & 11-20 =155 (then + together) = 210

And finally:

e) if 1-20 = 210 then 3-60 = 210x 3 = 630

• James O'Reilly says:

a) 165
11+20 = 31, multiply by 5 (5 pairs of 31)
b) 110
2+20 = 22, multiply by 5 (5 pairs of 22)
c) 100
1+19 = 20, multiply by 5 (5 pairs of 20)
d) 210
100 +110
e) 630
3+60 = 63, multiply by 10 (10 pairs of 63)