Problem of the Week Archive (2016/2017)

August 2017

What fraction of the hexagon is shaded?




2/3 of the hexagon is shaded.


July 2017


a. Which is greater 35% of 45 or 45% of 35?

b. Which is greater? An increase of 10% followed by a decrease of 10% or a decrease of 20% followed by an increase of 20%?

c. At a High School, 90% of the students take mathematics, 85% take science and 80% take geography. What percentage, at least, must take all three subjects?



a. The amounts are equal.

b. Increase of 10% followed by a decrease of 10%


June 2017

What number comes next?

7, 9, 16, 25, 41, 66





April 2017

The day before the day after tomorrow is Monday. What is the day before the day after yesterday?





Monday, 13 March, 2017

Four years ago Dad was eight times as old as Junior. Today he is only four times as old.

How old are they?



Dad is 28, Junior is 7.


Monday, 27 February, 2017

Kathy has eighteen pets altogether: mice, cats and budgies.

The cats have twice as many legs as there are budgies and ten more legs than there are mice.

How many are there of each type of pet?



6 mice, 4 cats and 8 budgies


Monday, 21 November, 2016


The problem is addition, each letter stands for a single digit. CAT is a prime number.

Find the value of each letter.









Monday, 14 November, 2016

Find the Age

Three boys were given 407 stamps, which were to be divided in proportion to their ages, the sum of which was 37 years.

Brian was given five stamps for every four John received and Bill was given five stamps for every six John received.

How old were the boys and how many stamps did each boy get?



The boys’ ages were 15, 12 and 10 and the numbers of stamps they had were 165, 132 and 110.


Monday, 25 October, 2016

What is the probability that a natural number less than 50 has exactly three factors?



Only four of the numbers between 1 and 50 have exactly 4 factors. These are 4, 9, 25 and 49 (note all are square numbers). Therefore the probability is 4/50 = 0.08.


Monday, 17 October, 2016

A particular month has 5 Tuesdays.

The first and the last day of the month are NOT Tuesday.

What is the last day of the month?



The last day of the month would be a Wednesday.


Monday, 12 September, 2016

A restaurant has a total of 30 tables which are of two types.

One type seats two people and the other type seats five people. When all of the tables are full the restaurant seats 78 people. How many tables seating two are there?



There would be 24 tables for two.


Monday, 29 August, 2016

I am a 2 digit prime number, less than 60 and the sum of my digits is 7. What number am I?



The number is 43.


Monday, 22 August, 2016

Which is the most rectangular country in the world?

The 'rectangularness' of a country as its maximum percentage overlap with a rectangle of the same area.

(see if you can get the answer without using Google – look at a map of the world!)



Egypt is the most rectangular country in the world (New Zealand was 156th)

(Defined by amount of overlap of land with a rectangle.)


Monday, 15 August, 2016

The average of n whole numbers is 80. One of the numbers is 100.

After removing the number 100, the average of the remaining numbers is 78.

Find the value of n.



The value of n is 11.


Monday, 27 June, 2016

How many cars?

A garage has less than 50 cars.

The manager arranges the cars in rows.

When he puts 6 cars or 4 cars in each row, there are no cars left over.

When he puts five in each row there is only one left over.

How many cars does the garage have?



The garage has 36 cars.


Monday, 9 May, 2016

Paint sells for $3 a litre and paint thinner sells for $1 for 3 litres.

A painter gave his helper $10 and two empty cans, telling him to bring back an equal

quantity of pain and thinner and that the $10 was to cover the total cost exactly.

What quantity of each item did the painter’s helper get?



The helper would buy 3 litres of paint and 3 litres of thinner.


Monday, 11 April, 2016

Anne is older than Annabel but younger than Anna.

Anna is one month older than Annaliese.

Annabel is two weeks younger than Anna.

Who is the eldest? Arrange the girls in order of age.



Anna is the oldest, followed by Anne, Annabel and Annaiese


Monday, 4 April, 2016

Which number am I

A multiple of two, that I be

Not odd but even you see

My digits a pair

When multiplied these, make a cube and a square out of me.



The number is 88


Monday, 21 March, 2016

I’m a five digit number.

All of my digits are odd.

I am not divisible by 5

My 1 is neither next to 3 nor to 7

My 3 is next to 5

I neither start nor end in 9 or 1

My middle digit is not a prime number.

The sum of my first two digits is half the sum of my last two.



31,597 is one solution. There are others.


Monday, 7 March, 2016

Each letter stands for a different digit.

The bottom line is the SUM of the four lines above.

Find the digit represented by each letter.









A = 2

B = 3

C = 4

D = 8

E = 9


Monday, 29 February, 2016

Mrs Alpa, Mrs Beta and Mrs Gamma teach English, mathematics and geography but not necessarily in that order.

Each has one son. The sons’ names are Tom, Dick and Harry, again not necessarily in that order.

Use the following information to work out the subject that each teacher teaches and the names of their sons.


Mrs Gamma is older than Harry.

Mrs Beta and the geography teacher are twins.

The mathematics teacher and Harry are the same age.

Mrs Gamma is Tom’s godmother and lives next door to the geography teacher.

Mrs Beta’s son is in the same class as Dick.



Mrs Gamma – Geometry – Dick

Mrs Beta – Mathematics – Tom

Mrs Gamma - English - Harry


Monday, 22 February, 2016

All ten digits are used in this cross-sum. What are they?




A = 4, B = 2, C = 7, D = 6, E = 3, F = 5, G = 8, H = 1, K = 0, J = 9


Monday, 8 February, 2016

Find the misfit on each line:

  1. 7, 17, 27, 37, 47
  2. Newton, Russell, Archimedes, Cayley, Napier
  3. circle, triangle, quadrilateral, pentagon, hexagon
  4. 36, 49, 81, 121, 164, 196
  5. 1, 100%, x0, 11/11, 0, 0.9999...
  6. m2, 0.5bh, πd, 0.5(a + b), 2πrh



The mis-fits were:

a. 7, 17, 27, 37, 47 (27 is a composite number, the rest are prime numbers.)

b. Newton, Russell, Archimedes, Cayley, Napier (Archimedes lived BC, the rest were AD)

c. circle, triangle, quadrilateral, pentagon, hexagon (circle is the only non-polygons, the rest are polygons.)

d. 36, 49, 81, 121, 164, 196 (164 is NOT a square number, the rest are.)

e. 1, 100%, x0, 11/11, 0, 0.9999… (0.9999… is not equal to exactly 1, the rest are.)

f. m2, 0.5bh, πd, 0.5(a + b)h, 2πrh (πd is the circumference of a circle, not an area, the rest are areas.)


Monday, 1 February, 2016

A bag contains identical sized balls of different colours. 10 red, 9 white, 7 yellow, 2 blue and 1 black.

Without looking into the bag, Peter takes out the balls one by one from the bag.

What is the least number of balls that Peter must remove from the bag to ensure that at least three have the same colour?



10 balls must be taken out to ensure each is of the same colour.