[SOLUTION]
3. Granny’s meter
Yesterday, the reading on Granny’s electricity meter was 098657. She was shocked to realise that all six of these digits are different.
How many more units of electricity will she use before the next time all the digits are different?
4. Paper folding
Three shapes X, Y and Z are shown below.
A sheet of A4 paper (measuring 297 mm × 210 mm) is folded once and placed flat on the table.
Which of these shapes could be made?
5. How many triangles?
In total, how many triangles of any size are there in the diagram?
6. Four dice
Rory uses four identical standard dice to build the solid shown in the diagram.
Whenever two dice touch, the numbers on the touching faces are the same. The numbers on some of the faces of the solid are shown.
What number is written on the face marked with an asterisk?
(On a standard dice, the numbers on opposite faces add to 7.)
7. Making 73
Taran thought of a whole number and then multiplied it by either 5 or 6. Krishna added 5 or 6 to Taran’s answer. Finally Eshan subtracted either 5 or 6 from Krishna’s answer.
The final result was 73. What number did Taran choose?
8. Decimal time
In the late eighteenth century, a decimal clock was proposed in which there were 100 minutes in each hour and 10 hours in each day.
Assuming that such a clock started at 0.00 at midnight, what time would it show when an ordinary clock showed 6 o’clock the following morning?
9. One size fits all
Harry’s mathematical grandmother keeps a large bag of ‘one size fits all’ socks in a dark cupboard. There are socks in red, blue, pink and green.
How many socks must she pull out to be sure of having a matching pair?
10. Cut the net
The diagram represents a rectangular fishing net made from ropes knotted together at the points shown.
The net is cut several times; each cut severs precisely one section of rope between two adjacent knots.
What is the largest number of such cuts that can be made without splitting the net into two separate pieces?
11. Times are changing
On a digital clock displaying hours, minutes and seconds, how many times in each 24-hour period do all six digits change simultaneously?
12. Making axes
In the addition sum shown, each letter represents a different non-zero digit.
What digit does each letter represent?
13. Roundabout
Four cars enter a roundabout at the same time, each one from a different direction, as shown in the diagram.
Each car drives in a clockwise direction and leaves the roundabout before making a complete circuit. No two cars leave the roundabout by the same exit.
How many different ways are there for the cars to leave the roundabout?
14. True or false?
None of these statements is true.
Exactly one of these statements is true.
Exactly two of these statements are true.
All of these statements are true.
How many of the statements in the box are true?
The team photograph
A photograph is to be taken of the school mixed five-a-side football squad, which includes three substitutes. The girls in the squad are Liz, Jenny, Sarah and Tracey. The boys are Alan, Matthew, Peter and Steve.
