# Making Maths Count

## Maths Week Scotland 2019 – Sums

October 2, 2019 by John Swinney MSP 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

Tags: John Swinney, Maths Week

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

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)