How many rectangles, how many routes — counting something easier that gives the same answer.
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A road divider is painted in repeating segments: white 2 m, black 5 m, white 2 m, black 5 m, and so on, beginning and ending with white. If the road divider is 149 m long, how many white segments are there?
[white 2m][ black 5m ][white 2m][ black 5m ][white 2m] ... |<----- one repeat = 7 m ----->| the whole divider is 149 m
Bob wrote letters in a repeating pattern: Z E S T Z E S T Z E S T Z E … How many letters ‘Z’ and ‘T’ are there altogether if there is a total of 87 letters in the whole series?
Z E S T Z E S T Z E S T Z E ... |<- one repeat = 4 letters ->| 87 letters altogether
A length of sticky tape is made up of repeated designs: a 5 cm striped band, then a 3 cm checked band, then a 4 cm grid band, repeating. The sticky tape is 80 cm long. How many checked bands are there altogether?
| striped | checked | grid | striped | checked | grid | ... |<- 5 cm ->|<- 3 cm ->|<-4cm->| |<-------- one repeat = 12 cm -------->| the whole tape is 80 cm
Some circles and triangles are arranged in a repeating pattern: triangle, circle, circle, circle, triangle, circle, circle, circle, triangle, … How many circles are there if there are 122 shapes?
/\ O O O /\ O O O /\ ... |<- one repeat = 4 shapes ->| (1 triangle and 3 circles)
There are 17 pupils in a class. The teacher gets each pupil to give a hi-five to every classmate once. How many hi-fives are exchanged altogether?
Jean is watching a movie in a hall. The chairs are arranged in rows with the same number, and all are occupied. There are 7 people behind Jean and 4 people in front of her. There are 3 people on her left and 4 people on her right. How many people are watching the movie?
7 behind
|
3 left --- JEAN --- 4 right
|
4 in front
(towards the screen)Study the staircase pattern: Figure 1 has 2 squares along the bottom and 1 above the right-hand one (3 squares). Figure 2 has 3 along the bottom, then 2, then 1 (6 squares). Figure 3 has 4, then 3, then 2, then 1 (10 squares). Find the total number of squares needed to form Figure 50.
Figure 1 Figure 2 Figure 3
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3 6 10 squaresSam had three coins in his wallet. They could be 10-cent coins, 20-cent coins or 50-cent coins. How many different possible amounts of money could Sam have in his wallet?
Mrs Bala wanted to sew 6 ribbons on each side of a square handkerchief. There was a ribbon at each corner of the handkerchief. How many ribbons did she sew in total?
R--R--R--R--R--R | | 6 ribbons along EACH side, R R one at each corner | | R--R--R--R--R--R
Jamie decorated a square classroom of side 6 m 40 cm. She tied balloons in a repeating pattern on a string and hung the string around the classroom once. In every 80 cm of string the pattern holds 4 small balloons (with big balloons between them). How many small balloons did she use to decorate the 4 sides of the classroom?
(BIG) o o (BIG) o o (BIG) |<--------- 80 cm --------->| o = small balloon · 4 small balloons in every 80 cm
A farmer planted some trees in a straight row, at an equal distance apart from one another. The distance between the 2nd tree and the 5th tree was 2340 m. What was the distance between the 1st tree and the 10th tree?
T1 T2 T3 T4 T5 ... T10
|<--------------->|
2340 m
the trees are equally spaced
(count the SPACES between them, not the trees)John divided the corridor of a school building into equal parts of length 4 m, and placed 2 potted plants in each part. For the same corridor, he divided it into equal parts of length 6 m and hung 5 lanterns in each part. If there were 24 more lanterns than potted plants, how long was the corridor?
Figure 1 |<-- 4 m -->| 2 potted plants in each part Figure 2 |<--- 6 m --->| 5 lanterns in each part
How many rectangles are there in the figure below?
┌───┬───┬───┐ │ │ │ │ └───┴───┴───┘
How many rectangles are there in the figure below?
┌───┬───┐ │ │ │ ├───┼───┤ │ │ │ └───┴───┘
How many ways are there from A to B, moving only up or right along the lines?
┌───┬───┐ B
│ │ │
├───┼───┤
│ │ │
A └───┴───┘How many ways are there from A to B, moving only up or right along the lines?
┌───┬───┐ B
│ │ │
├───┼───┤
│ │
A └───┘How many squares are there in the figure below?
┌───┬───┬───┐ │ │ │ │ ├───┼───┼───┤ │ │ │ │ ├───┼───┼───┤ │ │ │ │ └───┴───┴───┘
In the same 3-by-3 figure as the question above, how many rectangles are there that are NOT squares?
┌───┬───┬───┐ │ │ │ │ ├───┼───┼───┤ │ │ │ │ ├───┼───┼───┤ │ │ │ │ └───┴───┴───┘
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