Some Questions to Ponder Solutions

1. 1 defeat
2. South
3. Wednesday
4. Dipesh (He ate 50 biscuits.)

The Two Jars Puzzle *****

Given a 5-litre jar and a 3-litre jar and an unlimited supply of water, how do you measure out 4 litres exactly?  (You can use as much water as you would like but you only have these two jars!)

Extension:  Are there any quantities you can’t make with these two jars?

Some Questions to Ponder ****

1. Bognor Rocks FC have a total of 15 points after 6 matches.  In their league, teams get 3 points for a win, 1 point for a draw and 0 points for a defeat.  How many defeats did they have?

2. I am on top of a helter-skelter facing east.  The chute will turn be anti-clockwise through 630^o.  In which compass direction will I be facing at the bottom?

3. If the day before the day before yesterday was Thursday, what is the day after the day after tomorrow?

4. Amy, Ben, Cleo, Dipesh and Emil each has a tin of biscuits.  There are 60 biscuits in each tin.  Amy eats 60% of a tin, Ben eats 48 biscuits, Cleo eats half a tin, Dipesh eats 5/6 of a tin and Emil eats 0.75 of a tin.  Who eats the most biscuits?

Questions were taken from the 2014 Primary Maths Challenge.

Prime Cube Solution

Here is a solution using 2, 7 and 9 in the positions given:

2	8	3
4	6	9
7	5	1

  

And here are two other solutions, although there are sixteen possible solutions:

2	8	1
6	4	7
9	5	3

2	8	3
6	4	9
5	7	1

Prime Cube ****

Write the numbers 1 to 9 into the squares of a 3x3 grid so that each row and column adds up to a prime number.  It does not have to be the same prime number each time.  There are 16 different solutions.  At least one solution uses the numbers as they are placed in the example below.  How many solutions can you find?

2
		9
7

Helpful Hint:  Draw a blank 3x3 grid.  Then cut out little squares of paper with the numbers on them so you can move them around on the grid to try different possibilities until you find a solution.

Roly Poly **

The dots on opposite faces of a die add up to 7.

1. Imagine rolling one die.

The score is the total number of dots you can see.

You score 17.

Which number is face down?

How did you work out your answer?

2. Imagine rolling two dice.

The dice do not touch each other.

The score is the total number of dots you can see.

Which numbers are face down to score 30?

Roly Poly Solution

1. The total number of dots on the dice is 21. Of these dots 17 are showing, so the face with 4 dots is face down.

2. The total number of dots on two dice is 42, so 12 dots are hidden. The two hidden faces must each have 6 dots.