## Problem of the Week Archive (2015)

 Monday, 14 December, 2015 An easier problem this week. Eleven years ago, why was the fifth minute after 8 o’clock in the evening on the third Tuesday in the fourth month so special?   Answer The time, date and year would all have been 2004, 2004, 2004
 Monday, 7 December, 2015 Ten years ago the ratio of John’s age to Peter’s age was 5:2. The ratio is 5:3 now. What will be the ratio in 10 years time?   Answer 10 years later the ratio will be 10:7
 Monday, 23 November, 2015 Find the next two numbers and the 20th number in the following sequences a. 19, 23, 27, … b. 3/4, 1/4, - 1/4, … c. 1, 10, 100, … d. 9, 18, 27, … e. 1, 3, 7, …   Answer a. 31, 35 and the twentieth term is 95 b. -3/4, -5/4 and the twentieth term is -8.75 c. 1000, 10,000 and the twentieth term is 1.0 x 1019 d. 36, 45 and the twentieth term is 180 e. 15, 31 and the twentieth term is 1,048,575 The King will make \$110 profit.
 Monday, 9 November, 2015 The King pays \$1000 for a horse. He sells it to one of his soldiers for 10% profit. The soldier later sells the horse back to the King for a 10% loss. How much profit does the King make altogether?   Answer The King will make \$110 profit.
 Monday, 19 October, 2015 Mr Driver, Mr Gardener, Mr Painter and Mr Shearer are a driver, a gardener, a painter and a shearer, but none of them have a name which corresponds to their occupation. The shearer is not Mr Driver, the gardener is not Mr Painter and neither Mr Gardener nor Mr Painter is the driver. Match each man with his occupation.   Answer Mr Driver is the gardener. Mr Gardener is the painter. Mr Painter is the shearer. Mr Shearer is the driver.
 Monday, 12 October, 2015 Rights and Wrongs “How many did you get right, Viv?” “I got 5 right” replied Viv. “No, she got fewer than 5” said Kathy. “Well, I know she got more than 0” said Linda. “Actually she got more than 5 right” said Carmen. Only one person was telling the truth.   Answer Viv got none right.
 Monday, 21 September, 2015 1/7 of a group of students score an A for Mathematics, 1/3 of the students score a B, ½ score a C and the rest score a D. If a total of 100 students score an A or B, how many students score a D?   Answer 5 Score a D grade.
 Monday, 14 September, 2015 m and n are two positive whole numbers and m + n < 10 (m plus n is always less than 10). How many different values can the product mn (m multiplied by n) have?   Answer There would be 16 possible values.
 Monday, 7 September, 2015 Family Dilemma In a family a boy has as many sisters as he has brothers, but each sister has only half as many sisters as brothers. How many children are there in the family?   Answer There would be 3 boys and 4 girls.
 Monday, 31 August, 2015 Exponential Homework A teacher gave homework to her class and and told her students that on each day after the first, they must do twice the number of problems they had done so far. If, at the end of 5 days they had completed one third of the problems, how long will it take to do ALL of the problems?   Answer   It would take 6 days to answer all the problems.
 Monday, 24 August, 2015 Numbers A In how many ways can 90 be written as the product of two consecutive whole numbers?   Answer   Only one 9 and 10   Numbers B In how many ways can 75 be written as the sum of at least two whole numbers all of which are consecutive?   Answer   There are 3 ways: 37 and 38, 24 25 and 26, and 13 14 15 16 and 17
 Monday, 17 August, 2015 Pets 1 How many pets has Anna got if all except two are cats, all except two are dogs, and all except two are hamsters?   Answer   Anna has three pets, one cat, one dog and one hamster.   Pets 2 At Alan's home there are chickens and sheep. Altogether there are 10 animals and 36 legs. How many sheep are there?   Answer   Alan has three sheep and 2 chickens.
 Monday, 10 August, 2015 THINK My digits they make up a pair, Whose sum and difference is a square, When multiplied they reach a score, And when pronounced they rhyme with door. What number am I?     Answer   The answer is 54
 Monday, 3 August, 2015 IF If odd numbers are purple and even numbers are yellow, what colour is an odd number plus an even number? What colour is an odd number plus an odd number? What colour is an even number plus an even number? What colour is an even number plus an odd number? Answer   a) Yellowb) Yellowc) Purple
 Monday, 27 July, 2015 Teacher's Age Four children were trying to guess their teacher’s age. Their guesses were 23, 28, 34 and 45 years. With a smile, the teacher told them that none of them had found his exact age. However to give them a hint, he told them that his age was between the highest and lowest of their guesses, and remarkably, the errors of their four guesses gave a total equal to his age. How old was the teacher? Answer   The teacher's age is 40.
 Monday, 22 June, 2015 Digital Dial-Up Jack is distraught. He can't remember Jill's telephone number. However, he does recall that all four digits are different and that the sum of the first two digits is 17. He also remembers that the sum of the middle pair of digits is 9, and that the sum of the first and last digits is 10. What number should he dial to restore his happiness? Answer   The number he should dial is 8902.
 Monday, 15 June, 2015 Slippery Sue When seven people asked Susie her age, her seven replies were: “I’m a teenager” “I’m not 9” “I’m 13” “I’m 12” “I’m 9” “I’m not 12” “My age is not an odd number” Susie had in fact given her age, but she had also told five lies. How old is she? Answer   She is 9 years old
 Monday, 8 June, 2015 Fencing Farmer Farmer Dagg planned his fence so that the posts would be exactly two metres apart but found he had five posts too few to build it this way. By placing the holes three metres apart, he had precisely the right number of posts for the fence. How long was the fence? Answer The fence is 30 metres long Neighbours Joe and Linda live next door to one another. The product of their house numbers is 2703. What are the house numbers? Answer The numbers were 51 and 33
 Monday, 1 June, 2015 Who's the tallest? Three friends, Peter, Ronald and Sandra are standing beside a stone wall. When Peter stands on Ronald's shoulders he can just see over the wall. When Ronald stands on Sandra's shoulders he does not quite reach the top of the wall. When Sandra stands on Peter's shoulders she can see over easily. Who is the tallest of the three friends? Answer Peter is the tallest Monkeys and LionsSandra keeps monkeys and lions. She lives in Africa. Her pets have a total of 80 feet and 24 heads. How many lions does she have? Answer There are 16 lions and 8 monkeys.
 Monday, 25 May, 2015 Number Work a. How many prime numbers from 1 to 100 contain the digit 1? Answer There are 8. They are 11, 13, 17, 19, 31, 41, 61, and 71 b. p and q are prime numbers. p is less than q. p + q is also a prime number. What is the value of p? Answer p = 2 and q = 3   c. I am a multiple of 6 and also a multiple of 4. The sum of my digits is a prime number. What number am I? Answer I am 12 Seeing the light Draw a diagram to show how you can arrange twelve lamp-posts in six rows, each with four lamp-posts. Clue: This puzzle will have you seeing stars! Answer A star shape with lamp posts on each of the six vertices (points) and six on the hexagon in the middle.
 Monday, 18 May, 2015 Biscuits A recipe for biscuits shows that to make 35 biscuits I will need 2 cups of flour. I want to make 210 biscuits for lunches next week. One packet of flour contains 5 cups of flour. How many packets of flour do I need? Answer You would need 2.4 packets (12 cups) JarsTwo identical containers are filled with mixtures of paint and water in the ratio of 2:1 and 3:1 repectively. If both containers are poured into another larger container what is the ratio of paint to water? Answer The ratio would be 17:7