48
Fun problems and puzzles
Textbook: pp. 126–127
GoalLearn to solve logic puzzles.
New words
puzzle · boshqotirmadrawing in one stroke · qalamni uzmay chizishequal parts · teng bo‘laklarlogical thinking · mantiqiy fikrlash
Explanation
Puzzle problems have no ready formula: draw, try several approaches and find the pattern. Rule for drawing a figure in one stroke without retracing any segment: it can be done if the number of points where an odd number of segments meet is 0 or 2. Passing through an intermediate point uses two segments, so only the start and end points may be odd. Another useful method is finding a number pattern, for example counting how many sticks are needed when each new square is added. When practising with sticks, do not break them and avoid sharp objects.
Worked examples
A square with both diagonals: at each corner 3 segments meet (odd), so there are 4 odd points — it cannot be drawn in one stroke.
A row of 5 squares from sticks needs 4 + 3 · 4 = 16 sticks (4 for the first, 3 more for each next).
Class activity
“Stick puzzle”: make 4 equilateral triangles from 6 identical sticks (in space — a triangular pyramid). With an adult, do not break the sticks.
Practice
1
How many triangles are there in a square with both diagonals drawn?
8
2
A point D is taken on side BC of △ABC and AD is drawn. How many triangles are in the figure?
3
3
A row of 7 squares is made of sticks. How many sticks are needed?
22
4
Why can a figure with 4 odd points not be drawn in one stroke?
Only the start and end points can be odd (two in all).