Sum Puzzles Notes on Investigation

There are three ways to solve these puzzles

1) Trial and error

2) Simple logic

3) Algebra

Using logic reason like this;

Step 1 If there are 100 stones altogether and 67 are in the circle

Then there must be (100 – 67) outside the circle

Therefore there must be 33 in the triangle but outside the circle

.

Step 2 If there are 59 in the triangle

Then there are (100 – 59) outside the triangle

Therefore there must be 41 outside the triangle but inside the circle

Step 3 Therefore there must be 100 – (33 + 43) in the intersection

Using algebra

Let the numbers in each part be a, b, c

Then (1) a + b + c = 100 (100 pebbles altogether)

(2) a + b = 67 (67 in the circle)

(3) b + c = 59 (59 in the triangle)

Substitute (2) in (1) Substitute (3) in (1)

(a + b) + c = 100 a + (b + c) = 100

67 + c = 100 a + 59 = 100

c = 33 a = 41

Substitute for a (2)

41 + b = 67

b = 26

So this simple puzzle can be used at almost any level and the kind

of solution suited to their ability to reason and use symbols.