Answers

Creativity Progressive matrices test

1 (i) D: Working round the block of four squares clockwise the figure rotates 90° clockwise and the outside dot alternates white/black.

(ii) D: Working round the block of four squares clockwise, the black triangle is reducing in size and the white triangle is increasing in size.

(iii) F: Each square contains three components, inner circle, outer border and middle border. In each row and column these three components are shaded black once each.

(iv) B: Looking across and down only lines common to both the first two squares are carried forward to the third square.

(v) D: Looking across and down the contents of the third square are determined by the contents of the previous two squares. Lines which appear in these first two squares are carried forward to the final square, except where lines appear in the same position in these two squares, in which case they are cancelled out.

(vi) C: So that one of the four different symbols appears in each row and column.

(vii) D: Looking at rows and columns, another circle (or ring), either black or white is added to alternate squares.

(viii) C: Looking along rows, the circle moves from side to side clockwise and, looking down columns, the circle moves to a different side anti-clockwise; in other words, in each row and column the circle is in one of the four different possible positions.

(ix) D: If you draw a line down the middle of the matrix vertically, the left-hand side is a mirror image of the right-hand side.

(x) A: So that the left-hand top block of four squares is identical to the right-hand bottom block, and the right-hand top block is identical to the left-hand bottom block.

Rating:

10 exceptionally creative 9 very creative 7-8 well above average 5-6 above average 3-4 average

Symbolic interpretation

2 You can mark this test yourself, however, it is best marked by a friend or family member.

Award one mark for each recognizable sketch, providing it is not similar to any of the other sketches. For example, if you draw a face, a second face scores no point as each sketch must have an original theme. You thus obtain marks for variety. If you are creative you will tend to try to draw something different for each sketch.

There is no correct answer to each of the six sketches as for each there is a considerable number of different possible ideas.

Rating

9 exceptionally creative

7-8 very creative

4-6 average

The test can be repeated any number of times either by using the same symbols provided or by using new symbols or lines of your own invention as starting points.

Lateral thinking word puzzles

3 (i) They contain two consecutive sets of double letters, for example: Carolina Allspice.

The letters which appear are the first two letters in the series first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth, eleventh, twelfth.

(iii) hand: words in column A can be prefixed with OLD: old faithful, old master, old soldier, old fashioned, old hand. Words in column B can be prefixed with NEW: new broom, new born, new moon.

(iv) biography

The letters ABCDEFGH are contained in the words in the same position as they are in the alphabet, for example, the eighth letter in biography is H, which is the eighth letter of the alphabet.

Take the initial letters of each word to form words reading both across and down:

DEAR RARE ASIA WEAR

(vi) They all contain three consecutive letters of the alphabet in reverse order, for example: the Common Market (onm)

Read down from top to right to spell out the words: arcane, crane, near, ran, an, a.

(viii) They all form words when a letter is deleted from the end one at a time, for example, herons, heron, hero, her, he and notes, note, not, no.

(ix) elope ruler (Peru) formal tacit (Malta) governor wayfarer (Norway)

(x) Insert numbers into each group of letters to form a word:

LISS + ONE = LIONESS NERK + TWO = NETWORK WED + EIGHT = WEIGHTED ZASS + NINE = ZANINESS EXD + TEN = EXTEND

The circles of your mind

4 If you study the design carefully you will see that regular patterns of circles appear in the three circular rings in order to give the whole design symmetry. For example, in the middle ring, every fourth circle contains a dot, every fourth circle contains a stripe and every sixth circle is black. The remaining circles are white, which lie directly opposite each other.

Divergent ability

5 Scoring and analysis:

You can mark your efforts yourself, but it is better if you get a friend or family member to do so.

Allow:

2 points for any good or original answer 1 point for a good attempt 0 points for completely impractical answers

Rating:

18-24 highly creative

13-17 above average

7-12 average

Now repeat the exercise as many times as you wish using other everyday objects, for example, a paper clip or an A4 piece of cardboard.

Rebuses

(iii) Short measure

(iv) Square meal

1 backwater

2 brainwave

3 groundhog (G round hog)

4 laundrette (la under ette)

5 backgammon

6 printout (pr in tout)

(vi) Familiar phrases

1 world without end

2 simple fracture

3 central nervous system

4 winds of change

5 next to nothing

6. tree of knowledge

7 quarter sessions

8 to go over board

9 mixed doubles (lobsdue is an anagram of doubles)

10 through thick and thin

11 fall flat

12 chief constable (chief cons table)

The hidden star

Lateral thinking number puzzles 8 (i) 6

The three numbers appearing in the same position in the three squares all add up to 10.

Each number represents the numbers in the same line across and the same line down, for example,

11 means one other number in the same line across and one other number in the same line down.

Add the first two numbers and then reverse the rest.

Take the difference between the sum of numbers circled and numbers not circled in overlapping circles. This produces the number in each overlapping segment.

In each line, the numbers in inverted and upright triangles total 16.

The numbers in the bottom half are the sum of the digits of the numbers in the top half as shown below:

Start at the top and work from left to right, then back along the second row right to left, etc, repeating the digits 58236.

The diagram shows a die being rolled from side to side through four turns from top to bottom.

Looking top left to bottom right, add even numbers only to obtain the first part of the middle number. Looking top right to bottom left, add odd numbers only to obtain the second part of the middle number. That is: 6 + 8 + 4 = 18 and 5 + 1 + 7 = 13.

Situation puzzles 10 Explanations:

(i) He is an official delivering a last-minute pardon to a prisoner on death row. The flicker of the lights indicated that the prisoner has just been electrocuted and the pardon has arrived too late.

(ii) The man is a postman delivering mail to the capitol's foreign embassies.

(iii) The two men started at opposite sides of the trench digging towards each other, but instead of meeting in the middle they dig right past each other because one of them has failed to dig in a straight line. Their boss confirms that one man was right after inspecting the plans and orders that the other man must re-dig his half of the trench.

(iv) Doris was a pet mouse sitting on a chair. Alan was playing musical chairs and sat down quickly when the music stopped, not noticing that Doris had climbed on to the chair.

(v) Harry is a child. Last year he could only reach the 11th floor button. This year he can reach the 12th floor button.

(vi) They are in a drive-in movie, so the crime goes undetected.

(vii) The man was a night-watchman who should have been on duty last night, and not dreaming.

(viii) It is a baker's shop in France. The French word for bread is pain.

(ix) I am driving my car in reverse.

(x) He is sitting on the window ledge inside his room.

The second circle moves to the bottom at the next

Looking across and down, any lines common to the first two squares are not carried forward to the end square, but all other lines are carried forward.

Sequential patterns 11 (i)

stage.

Each row and column contains a black centre, a black middle ring, a black outer ring, a black dot below the main circle and a white dot at the top.

Looking across, the top dot alternates white/black, the dot in the ellipse alternates black/cross and the dot below alternates white/striped/black.

Looking across, the arc rotates 90° clockwise and looking down it rotates 90° anti-clockwise.

The figure is rotating 90° clockwise and every alternate figure has a black dot.

Looking across and down only dots common to the first two squares are carried forward to the third square.

The top dots are moving a corner at a time clockwise and the bottom dots anti-clockwise. Both dots alternate black/white.

Adjacent figures are mirror images of each other.

Adjacent figures are mirror images of each other.

The triangle moves two sides anti-clockwise, the white dot moves one side clockwise and the black dot moves one side anti-clockwise.

Rating:

10 exceptionally creative 9 very creative 7-8 well above average 5-6 above average 3-4 average

Matchstick puzzles 12 (i)

Problem solving

Puzzles 1 63 = 216 Explanation:

If there was only one circular path the man could continue in three ways when first reaching the intersection (left, right or straight forward). On reaching the second intersection he would have the choice of just two routes, so that altogether there would be six (3 x 2) possible routes. If the number of circular routes were increased to two, the choice of routes is

62, or 36. With three circular routes the choice of routes is

63, or 216. This formula holds good for any number of circular routes.

o

■»7

o

\

o

\

o

Explanation:

Therefore: A + B + D + E must be twice the area of C + F.

4 27 Explanation:

Because opposite sides of a die always total 7, the bottom face of the top die must be 6 (7+1). Faces 2 + 3, 4 + 5 and 6 + 7 must all total 7. The total of the 7 faces is, therefore, 7 + 7 + 7 + 6 = 27.

5 Four people

Explanation:

My wife and I Keith, my son Jane, my sister-in-law

Jane's brother-in-law and his wife are my wife and I. My book editor Alex is my wife. Mrs Morgan is my sister-in-law Jane. Jane's nephew is my son Keith.

6 Two chances in three. Explanation:

Call the balls which may be put in the bag first W1 and B, and call the white ball that you see go in W2. After the white ball has been drawn out there are three possibilities remaining:

(a) W1 still in the bag W2 outside.

(b) W2 still in the bag W1 outside.

(c) B still in the bag W2 outside.

There are, therefore, only two of the three possibilities where the ball remaining in the bag is white, and one possibility where it is black.

7 14th floor. Explanation:

It was operating in the sequence 7, 9, 6, 11, 4, 12, 3, 14.

There were, therefore, two alternate sequences, up and down. The down sequence progressed -1, -2, -1, etc.; and the up sequence progressed +2, +1, +2, etc. It would take us to the 14th floor whether we liked it or not.

8 D Explanation:

Count the number of lines in each square. The number of lines in each horizontal, vertical and corner-to-corner line adds up to 15.

9 29347 Explanation:

Even numbers 6824 and odd numbers 93715 are being repeated in the same order.

10 See me at two by the cliff. Explanation:

be(see)ch, la(me)nt, C(at)hy, foo(two)rn, a(by)ss, wi(the)er, Heath(cliff)e

11 c

Explanation:

The top row is a mirror image of the third row, and the second row is a mirror image of the bottom row.

13 1 chance in 4900 Explanation:

50 49 48 117600 4900

The dots can be joined to produce the sequence of numbers 1 2 3 4 5 6 7.

15 B Explanation:

Looking across and down in each row and column the number of sides in each figure increases by 1 each time.

16 32 Explanation:

Triangles are formed as follows:

individual triangles

two segments

three segs.

four segs.

1

1/2

1/2/3

2/6/7/10

2

1/4

1/4/5

4/7/8/12

3

2/3

3/8/9

4

3/8

5/6/11

5

4/5

9/10/13

6

5/6

11/12/13

8

8/9

9

9/10

10

6/11

11

10/13

12

11/12

13

12/13

18 Four times faster Explanation:

I hobbled the last third of the way i.e. half as far as I ran, in twice the time.

For example, suppose the race was 12 miles long.

Then I ran 8 miles and hobbled 4 miles.

Say I ran at 8 mph and walked at 2 mph.

Then: 8 miles at 8 mph = 1 hour 4 miles at 2 mph = 2 hours

19 7 Explanation:

The middle two lines total 13, the second and fourth lines total 10 and the top and bottom lines total 7.

20 Mexico Explanation:

Take the Roman numeral value from the centre of each word and add; so that review + envoi = Mexico (vi + V = xi).

21 handsomely

22 JLNM Explanation:

All the others proceed in the sequence as, for example, LmNoQP where one letter is missed, then a further letter and the order of the last two letters is reversed.

23 358799 to 1 Explanation:

It is a 1 in 26 chance that the first card will be P, 1 in 25 that the second will be A, 1 in 24 the third will be U and 1 in 23 the fourth will be L.

The chances are 26 X 25 x 24 x 23 = 1 in 258800, or 358799 to 1.

The chances that the last four cards will spell P_A_U_L is exactly the same.

24 Make both ends meet. Explanation:

Take the first letters of the words in the top row, the second letter of the words in the second row, the third letter of the words in the third row and the fourth letter of the words on the fourth row to spell out the message.

Explanation:

In each row and column alternate pips add up to the same, for example, in the first row, 1 + 6 = 5 + 2.

Numerical problem solving

Explanation:

2 No

Explanation:

0+1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45 Since Jimmy has only 44 the answer is No.

3 18

Explanation:

Latin

French

German

Latin/French

French/German

Latin/German

Latin/French/German

10 29 17

100 less than 82 means that 18 students studied none of the three languages.

4

Hole

Geoff

Harry

£100

£0

1

WIN

£150

LOSE

-£50

2

WIN

£225

LOSE

-£125

3

LOSE

£112

WIN

-£13

4

TIE

£112

TIE

-£13

5

LOSE

£56

WIN

+£43

6

WIN

£84

LOSE

+£15

7

WIN

£126

LOSE

-£27

8

LOSE

£63

WIN

+£36

9

LOSE

£32

WIN

+£68

10

WIN

£48

LOSE

+£52

11

WIN

£72

LOSE

+£28

12

TIE

£72

TIE

+£28

LOSES

£28

WINS

£28

The reason is that if Geoff won every hole he would win thousands of pounds but Harry could only win the £100 in Geoff's wallet. So Harry would win even if he lost by a few holes, to balance the books.

5 As suggested in the hint, if you needed to use it, first, consider numbers between 200 and 300 that have different factors. For example, 240 fingers that could be:

20 aliens with 12 fingers or 12 aliens with 20 fingers or 10 aliens with 24 fingers or 24 aliens with 10 fingers

Not a unique answer, so all numbers having different factors are eliminated.

Now try prime numbers (a prime number is a number which has no factors except 1 and itself). For example, 233. That could be:

1 alien with 233 fingers (but there is more than

1 alien)

or 233 aliens with 1 finger (but each alien has at least

2 fingers)

Not a unique answer, so all prime numbers in the range are eliminated. That leaves only the square of a prime number.

There is only one between 200 and 300 and that is 289 = 17 x 17, so the answer is 17 aliens each with 17 fingers.

6 July

Alan

Barbara

Carol

David

Edward

Fiona

JAN

/

/

/

/

FEB

/

/

MAR

/

/

APR

/

/

MAY

/

/

JUN

/

/

JUL

/

/

/

AUG

/

SEP

/

/

OCT

/

/

NOV

/

/

DEC

/

/

As it is the only month with three ticks, the circus must be coming to town in July.

Explanation:

HORSE

ODDS

SANDS OF TIME

10-1

33.3

11.1

115.2

LITTLE BEN

MOONSHINE PHIL'S FOLLY

ABANDON ALL HOPE CATCH KEN

Therefore, as he pays out £100, he collects £115 and gives himself a 15% margin.

8 For a coin to fall within a square, its centre must fall within the shaded area. If it falls outside, it will touch a line. Therefore:

successful unsuccessful odds

1V2 x 1V2= 21/4 16-21/4 = 13% 133/4 : 21/4 55:9 against or odds of

h-2V2'H

Explanation:

The numbers are obtained by adding the digits, not the numbers, so the missing number is 12:

7 + 2 + 9 + 9 = 27 2 + 7 + 4 + 5 = 18 1 + 8 + 3 + 9 = 21 2 + 1 + 3 + 6= 12

10 56

8 2X2X2 7 ix7 4 3X3

Cross out the repeats, which completely eliminates the smallest cog from the equation.

11 64 diamonds and 8 sons

12 411/20 ft

Explanation:

If the height of the break is x: then

10 units

10 units

Explanation:

1

9 %

14

3

2

9

15

3

3

9

16

2

4

8

17

2

5

8

18

1

6

7

19

IV2

7

7

8

6

9

6

100 units

= 10 units2

10

5

11

5

Formula length of walk =

12

4

13

4

Answer =

: 60 ft = 3600 ft

Therefore, 239 cats each caught 4649 mice.

15 81

Explanation:

GREATER THAN 50

GREATER THAN 50

52-56 to 96-100

51-53 to 98-100

MULTIPLE OF 4

9-to 47

9-to 47

52-56 to 96-100

64-100 52-56 to 92-96

64-100 52-56 to 92-96

Thus, 81 is the only unique number.

16 1 x 1 x 1 x 3 x 13 x 13 x 13 = 6591 Including 2 sets of triplets.

17 To divide by 2.236 is tedious. Avoid this as follows:

18 8

The left-hand side of the equation is divisible by 9 (32), so the right-hand side must also be so.

The sum of the digits on the right-hand side is therefore divisible by 9, making ? = 8.

Note: a number is divisible by 9 exacdy only when the sum of its digits is exactly divisible by 9.

19 49 x 48 x 47 x 46 x 45 x 44 1x2x3x4x5x6

= 1006834752 720

20 19.2 sq yds

Let x = total area

Agility of mind

1 (0

leading/aligned

(ii)

COG and TOP

(iii)

28 (7 x 4)

(iv)

N

(V)

4 miles

(vii) moose

(ix) gambol

It is a right-angled triangle: 82(81) + 122 (144) = 152 (225)

(xi) 50mph (length of journey = 2 hours)

(xii) 70% (percentage of consonants)

(xiii) a square meal (breakfast)

(xiv) 25 minutes

12.35 less 20 minutes = 12.15

(xvi) China and Chile

(xix) engulf

The words begin and end with consecutive letters of the alphabet ABCDEFGH.

(xxi) academic, accompany, accordion, acropolis, address, adept, admission, adoration

(xxiii) athletic

(xxiv) P ABcDefGhijKlmnoP

Looking across the sequence is +4,-3. Looking down the sequence is +3,-2.

(xxvi) 13000 14000

1300 400

14313 14404

(xxvii) Angela

(xxviii) 70

Rating:

27-30

superb effort

24-26

excellent

20-23

very good

16-19

good

12-15

above average

9-11

average

2 (i)

The diamond moves round a notch at a time as does the black segment.

O

The white dot moves four segments round the rectangle anti-clockwise at each stage.

Add a white dot to the bottom, then a white dot to the top, then a black to the bottom and finally a black to the top.

The Roman numerals I, II, III, iy y VI appear turning 90° clockwise at each stage.

The figures alternate mirror image then blackAvhite reversal.

In each row the black segment is moving one segment clockwise.

The circles are moving from top to bottom in turn.

At each stage the figure next to top drops to the bottom.

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