Tash has a bag with 7 counters in it. Each counter is one colour, and there are 3 different colours in the bag. Tash says:“I’m most likely to pull out a red counter, and least likely to pull out a yellow one. I might pull out a purple counter, but with only a slightly better chance than yellow.”How many counters of each colour are in Tash’s bag?

4 red, 2 purple and 1 yellow - Seven counters, three colours, red the most, yellow the least and purple only just ahead of yellow. 4 + 2 + 1 is the only way to split 7 like that.

What fraction of this shape is shaded? Can you write it as a decimal too?

6/10 (or 3/5), which is 0.6 - The shape is split into 10 equal parts and 6 of them are shaded. Six tenths is 0.6 as a decimal.

Use each of the digits 3, 6, 1, 8 and 4 once to make a five-digit number that is:a) as small as possibleb) as large as possible

13,468 and 86,431 - For the smallest number, put the digits in order from smallest to largest. For the largest, go from largest to smallest.

What is the name of this polygon?

A heptagon - It has 7 sides. “Hepta” is the Greek word for seven.

There was a power cut at Oscar’s house and his digital clock lost time. It now reads 8:50am, but it is 35 minutes behind. What is the actual time?

9:25am - 10 minutes gets you from 8:50 to 9:00, and the other 25 minutes takes you to 9:25.

What are the two missing numbers in this pattern?11, 17, ?, 29, ?, 41 …

23 and 35 - Start at 11 and add 6 each time: 11, 17, 23, 29, 35, 41.

What is the size of angle x?

25° - Angles around a point add up to 360°. The square corner is a right angle (90°), so x = 360 − 135 − 90 − 110 = 25.

A boat is 8 km west of the harbour. It sails 7 km further west, then turns around and sails 11 km east. Where is the boat now?

4 km west of the harbour - 8 + 7 = 15 km west, then 11 km back towards the harbour leaves it 4 km west.

What is the area of this triangle?

34 m² - Area of a triangle = ½ × base × height = ½ × 10 m × 6.8 m = 34 m².

Imagine you have $1,000,000,000 (one billion dollars) to give away, and you hand out a $50 note every minute, day and night, without stopping. Roughly how long would it take to give it all away?

About 38 years - $1,000,000,000 ÷ $50 = 20,000,000 minutes. That’s about 333,333 hours, or 13,889 days, which works out to roughly 38 years.

Pam has a block of cheese that is 10 cm long, 10 cm wide and 10 cm tall. She wants to cut it into 1 cm cubes. What is the smallest number of straight cuts she needs, if she can’t stack or move the pieces between cuts?

27 cuts - 9 cuts one way, 9 cuts the other way, then 9 cuts from top to bottom. 9 + 9 + 9 = 27, and you end up with 1,000 little cubes.

A four-digit number has first digit 2.When the digits of the number are reversed, the resulting number is 4 times the original number.What is the original number?

2178 - The first digit of the reversed number must be 8 or 9, so the final digit of the original number must be 8 or 9. However, 8 is the only possibility, since the reversed number ends in 2 (8 x 4 =32). Since the reversed number starts with 8, the second digit of the original number must be 0,1, or 2. 1 is the only possibility, to ensure the reversed number is a multiple of 4 (ie it ends in 12). Since 21x4=84, the remaining digit must be at least 4. By trying each possibility, the correct option is 7. The original number is 2187, and 8712=4x2178.

A book’s pages are numbered consecutively starting from 1. In total, 408 digits are used to write all the page numbers. How many pages does the book have?

172 pages - The first 9 pages contain 1 digit each, for a total of 9 digits. The next 90 pages contain 2 digits each, for a total of 180 digits. The next n pages contain 3 digits each, for 3n digits in total. 9 + 180 + 3 n = 408 3n = 219 Therefore there are 9 + 90+ 73 = 172 pages

Two candles are the same length but made of different wax. One burns down completely in 4 hours, the other in 5 hours. Both are lit at exactly midnight. At what time will one candle be four times as long as the other?

3:45am - Call each candle 1 unit long. After t hours the 4-hour candle has 1 − t/4 left and the 5-hour candle has 1 − t/5 left. The slow one is four times the fast one when: 1 − t/5 = 4(1 − t/4) 1 − t/5 = 4 − t 5 − t = 20 − 5t 4t = 15 t = 3¾ hours 3¾ hours after midnight is 3:45am. Check: the fast candle has 1/16 left and the slow one has 1/4, exactly four times as much.

The hour hand and the minute hand of a clock are at a right angle. How long until they make a right angle again?

32 and 8/11 minutes (about 32 minutes 44 seconds) - Every minute the minute hand moves 6° and the hour hand moves ½°, so the gap between them grows by 5½° a minute. To get from one right angle to the next the gap has to change by 180°, and 180 ÷ 5½ = 32 8/11 minutes.

Maths Puzzle Quiz for Kids | Free Family Maths Quiz with Haese Mathematics

4 red, 2 purple and 1 yellow
Seven counters, three colours, red the most, yellow the least and purple only just ahead of yellow. 4 + 2 + 1 is the only way to split 7 like that.

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6/10 (or 3/5), which is 0.6
The shape is split into 10 equal parts and 6 of them are shaded. Six tenths is 0.6 as a decimal.
13,468 and 86,431
For the smallest number, put the digits in order from smallest to largest. For the largest, go from largest to smallest.
A heptagon
It has 7 sides. “Hepta” is the Greek word for seven.
9:25am
10 minutes gets you from 8:50 to 9:00, and the other 25 minutes takes you to 9:25.
23 and 35
Start at 11 and add 6 each time: 11, 17, 23, 29, 35, 41.
25°
Angles around a point add up to 360°. The square corner is a right angle (90°), so x = 360 − 135 − 90 − 110 = 25.
Haese Mathematics Readers. Building maths through storytelling
4 km west of the harbour
8 + 7 = 15 km west, then 11 km back towards the harbour leaves it 4 km west.
34 m²
Area of a triangle = ½ × base × height = ½ × 10 m × 6.8 m = 34 m².
About 38 years
$1,000,000,000 ÷ $50 = 20,000,000 minutes. That’s about 333,333 hours, or 13,889 days, which works out to roughly 38 years.

The last 5 are proper brainteasers.

27 cuts
9 cuts one way, 9 cuts the other way, then 9 cuts from top to bottom. 9 + 9 + 9 = 27, and you end up with 1,000 little cubes.
2178
The first digit of the reversed number must be 8 or 9, so the final digit of the original number must be 8 or 9. However, 8 is the only possibility, since the reversed number ends in 2 (8 x 4 =32).
Since the reversed number starts with 8, the second digit of the original number must be 0,1, or 2. 1 is the only possibility, to ensure the reversed number is a multiple of 4 (ie it ends in 12).
Since 21x4=84, the remaining digit must be at least 4. By trying each possibility, the correct option is 7.
The original number is 2187, and 8712=4x2178.
172 pages
The first 9 pages contain 1 digit each, for a total of 9 digits.
The next 90 pages contain 2 digits each, for a total of 180 digits.
The next n pages contain 3 digits each, for 3n digits in total.

9 + 180 + 3 n = 408
3n = 219
Therefore there are 9 + 90+ 73 = 172 pages
3:45am
Call each candle 1 unit long. After t hours the 4-hour candle has 1 − t/4 left and the 5-hour candle has 1 − t/5 left. The slow one is four times the fast one when:
1 − t/5 = 4(1 − t/4)
1 − t/5 = 4 − t
5 − t = 20 − 5t
4t = 15
t = 3¾ hours
3¾ hours after midnight is 3:45am. Check: the fast candle has 1/16 left and the slow one has 1/4, exactly four times as much.
32 and 8/11 minutes (about 32 minutes 44 seconds)
Every minute the minute hand moves 6° and the hour hand moves ½°, so the gap between them grows by 5½° a minute. To get from one right angle to the next the gap has to change by 180°, and 180 ÷ 5½ = 32 8/11 minutes.

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Maths Challenge

Fifteen maths puzzles from the team at Haese Mathematics. Specialists in mathematics education.

4 red, 2 purple and 1 yellow

6/10 (or 3/5), which is 0.6

13,468 and 86,431

A heptagon

9:25am

23 and 35

25°

Haese Mathematics Readers. Building maths through storytelling

4 km west of the harbour

34 m²

About 38 years

27 cuts

2178

172 pages

3:45am

32 and 8/11 minutes (about 32 minutes 44 seconds)

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