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5. How many triangles?
In total, how many triangles of any size are there in the diagram?
[SOLUTION] (#litres_trial_promo)
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.)
[SOLUTION] (#litres_trial_promo)
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?
[SOLUTION] (#litres_trial_promo)
Week 2 (#ulink_1016459e-b051-5406-97a6-6139c3793e01)
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?
[SOLUTION] (#litres_trial_promo)
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?
[SOLUTION] (#litres_trial_promo)
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?
[SOLUTION] (#litres_trial_promo)
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?
[SOLUTION] (#litres_trial_promo)
12. Making axes
In the addition sum shown, each letter represents a different non-zero digit.
What digit does each letter represent?
[SOLUTION] (#litres_trial_promo)
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?
[SOLUTION] (#litres_trial_promo)
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?
[SOLUTION] (#litres_trial_promo)
Logic Challenge 1 (#ulink_2d182eee-66a7-50cc-81d5-2e6005837b3b)
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.
The team line up in two rows of four. Read the clues below to work out who is standing where and what number they are wearing (which will be one of the numbers from 1 to 8).
Place the number in the top square of the answer grid and the name in the bottom square of each row.
The clues
Tracey is in the front row in front of Jenny.
The average of the two numbers in the middle of the front row is Sarah’s number, a square.
Peter is not sitting next to a girl.
Steve is sitting between Liz and Jenny.
Players with prime numbers, which includes Alan, are sitting in the front row.
There is only one boy on the end of a row.
In both the front and back rows the two places on the right (as you look at it) are filled by a boy and a girl.
Matthew and Steve have the highest and lowest numbers a boy could wear.
Jenny’s number is three times as large as Tracey’s and twice as large as that of Peter, who is not sitting on the end of a row.
Girls have even numbers.
Back row
Front row
[SOLUTION] (#litres_trial_promo)
Week 3 (#ulink_de5bc97f-d628-5f7b-a856-f997eaea0b93)
15. A line of lamp posts
Four lamp posts are in a straight line. The distance from each post to the next is 25 metres.
What is the distance from the first post to the last?
[SOLUTION] (#litres_trial_promo)
16. Sums of digits
For how many three-digit numbers does the sum of the digits equal 25?
[SOLUTION] (#litres_trial_promo)
17. A million seconds
How many days, to the nearest day, are there in a million seconds?
[SOLUTION] (#litres_trial_promo)
18. Sum to 100
The sum of 10 distinct positive integers is 100. What is the largest possible value of any of the 10 integers?
[SOLUTION] (#litres_trial_promo)
19. x marks the spot
The numbers 2, 3, 4, 5, 6, 7, 8 are to be placed, one per square, in the diagram shown such that the four numbers in the horizontal row add up to 21 and the four numbers in the vertical column also add up to 21.
Which number should replace x?
[SOLUTION] (#litres_trial_promo)
20. The last Wednesday
One of the months in a particular year has five Wednesdays, and the third Saturday is the 19th.
Which day of the month is the last Wednesday?
[SOLUTION] (#litres_trial_promo)
21. Her brother’s age
A woman says to her brother, ‘I am four times as old as you were when I was the same age as you are now.’
The woman is 40 years old.
How old is her brother now?
[SOLUTION] (#litres_trial_promo)
Week 4 (#ulink_cdf24422-70e9-5513-8bf6-454eb7dc2098)
22. Pings and pongs
Five pings and five pongs are worth the same as two pongs and eleven pings.
How many pings is a pong worth?
[SOLUTION] (#litres_trial_promo)
23. How many sides?
A single polygon is made by joining dots in the grid with straight lines, which meet only at dots at their end points. No dot is at more than one corner. The diagram shows a five-sided polygon formed in this way.
What is the greatest possible number of sides of a polygon formed by joining the dots using these same rules?
