## Challenge Your Creativity: 77 Problem Solving Exercises – Solutions

Here are the solutions to “Challenge Your Creativity: 77 Problem Solving Exercises”.

*The word Go made from jigsaw puzzle pieces by Horia Varlan.*

# Math & Probability Problems

### 1. Age

When Gerald is 12, Jane is 4.

So, when Gerald is **16** years old, Jane is 8 years old.

### 2. Sequence Problem

4x+y = 13

13x+y = 40

40x+y = 121

121x+y = n

x = 3

y = 1

**n = 364**

### 3. Replace X

X = 5

For each row the sum of the first two columns is equal to the multiple of the last two columns. For instance if we take the first row: the first two columns 7 + 9 = 16 which is the same as the two last columns when they are multiplied, 4 * 4 = 16.

### 4. Simplify Expression

= 2a - 6 + 4b -2a + 2b + 6 + 5

= **6b + 5**

### 5. Bakers' Cookies

It will take 625 minutes.

5 * 250 = 1250

1250/2 = 625

### 6. Middle Number

X = 30

In each set, the difference between the two leftmost numbers is divided by two, and then multiplied by the sum of the two rightmost numbers. The product is written in the middle for each set.

### 7. Fill in the Sequence

X = 28

8+1 = 9

9+1+2 = 12

12+1+2+3 = 18

18+1+2+3+4 = X=28

28+1+2+3+4+5 = 43

### 8. Majoring Students

**160 students.**

If 55 % of the students are statistics majors, we know that 45 % are not statistics majors. And if 77% of the students do major in business then 23 % are not business majors.

45 + 23 = 68 % of the students are not majoring in both statistics and business

Hence, 32% are double majors.

500 * 0.32 = 160 students.

### 9. Random Employee

There is a 48 % chance that the employee is a woman.

632 + 593 = 1225

593/1225 = 0.484...

100 * 0.484 = 48.4

### 10. Possible Outcomes

It's called a tree diagram.

### 11. Classic: Monty Hall Problem

The choice that would give the highest probability of winning would be to change the choice of door.

It’s easy to believe that there is a third’s chance of winning the car throughout the entire game. But this is not the case. The easiest way of explaining this problem is like this: the probability that you have chosen the right door from the beginning is 1/3. If you then later on choose to stay, your probability to win will remain to be 1/3. But if you choose to change door, the probability of winning would be 2/3.

Look at this list from Vos Savant, Marilyn (1990b) “Ask Marilyn” column *Parade Magazine* p.25. 2 December 1990.

### 12. Another Number Sequence

**n = 1295**

**1** + 2 = 3

1 * 3 = **3**

**3** + 2 = 5

3 * 5 = **15**

**15** + 2 = 17

15 * 17 = **255**

n = ((**255** + 2) * 255)

### 13. How Old is Elin?

Elin is 4 years old.

### 14. Placement of Cards

The three cards placed on the table are the king of spades, the queen of spades, and the queen of hearts.

### 15. Does not Belong

21 does not belong in the list of numbers because it is not a prime number.

### 16. Which Number?

12 does not belong because it's an even number while the others are uneven.

### 17. Next Number

X = 72

1*2 = 2

2*3 = 3

3*4 = 12

etc.

### 18. Symbol Sequence

A) = =

Because the first 5 symbols are repeated as a set.

### 19. Logical Symbol Sequence

B) 8 Y

### 20. Logical Sequence

C) - - - %

# Verbal Intelligence Problems

### 21. Rearrange and Categorize

It's a city (Shanghai).

### 22. Which Word?

The answer is d (engine).

### 23. Find the Answer

The answer is Infuriated.

As "Nonsensical" is synonymous with "Ridiculous ", similarly "Indignant" is a synonym for "Infuriated".

### 24. Matching

Aware and Conscious, as they can be used as synonyms.

### 25. Association

...as Magenta is to **Red**.

### 26. Remove 6 Letters

Yes.

### 27. Finding E

No, it's not true because "e" is not a consonant.

### 28. Makes Sense?

No the sentence doesn't make sense.

### 29. English Alphabet

The answer is **13**. (you don't include F and T)

### 30. Words found in Words

Yes.

### 31. Synonym

c) peevish

### 32. Association

...as Born is to **die**.

### 33. Missing Letter

The missing letter is J.

Change each letter to its numerical equivalent in the alphabet. For example the letter **F** is assigned to the number **6**. For each row, multiply the numerical equivalents of the first two columns to get the letter in the third column.

### 34. Alphabetical order

Jail.

### 35. Word Grid

### 36. Find the Letter

? = F

Convert each letter to its numerical equivalent in the alphabet, and then minus one.

For instance;

E = 5,

5-1 = 4

Then, for each row, multiply the numerical equivalents - minus 1 - of the first two columns in order to calculate the letter in the third column.

# Logical Intelligence Problems

### 37. The Ball

Throw the ball straight up in the air.

### 38. Make a Square

You get a square in the middle of the matches by pulling back the match to the right.

### 39. Months

All months have 28 days, at least.

### 40. What Day is It?

It's Tuesday.

### 41. Is to

...is to leaf.

### 42. Triangle Logic

X = 1649

4^2 = 16

7^2 = 49

16 <-> 49

### 43. Classic: Hand Shakes

**182 handshakes.**

The 1st person shook hands with 13 people. So did the 2nd person but we only count 11 because the hand shake with the first person has already been counted. And so it goes on: 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 91.

Hence 91 hand shakes took place before & 91 after the meeting, for a total of 182.

### 44. Mathematical Symbol

6**.** 9

### 45. Prove it

One way to do this is by using roman numerals:

19 = XIX

remove I and you have XX = 20

### 46. 615182021145

Fortune

5-18-1-19-5-18 each number in the break up signifies the corresponding letter in the alphabet. Hence 6-15-18-20-21-14-5 signifies fortune.

### 47. Shortest

Emma is the shortest.

### 48. Visual Logic

## Pattern Recognition Problems

### 49. Geometrical Shapes

B is different because the shape inside it is the same as itself while the other figures have different shapes.

### 50. Line of Drawings

The answer is C.

*The number of lines on the side with the stick goes increases by one, while the side opposite the stick decreases by one. The stick alternates sides.* - from Mensa.org

### 51. Comparison

Lamina is Animal backwards.

Hence, the correct answer for 46251, is **15264**.

### 52. Outsider

The snake, it doesn't have four legs.

### 53. Read Colors

This can be somewhat difficult because the exercise is using both of your brain halves. The right brain half is trying to “read” the colors, while the left is trying to read the words.

### 54. Favorite Numbers

Mark doesn't like the number 5628 because the digits add up to 21. While the other numbers add to numbers that can be squared.

### 55. Letter Design

H is least like the others, because it is made out of 3 lines while the others are made out of 4 lines.

### 56. Flower Patterns

The answer is E.

*The first column has 6 'petals', while the second has 5. The first row is solid. The second row has lines going from the 'petals' into the center.* - from Mensa.org

### 57. Word Play

**KORCEV** is the correct answer, as each letter in the word REASON is forwarded two places (+2) in an alphabetical order, to attain TGCUQP.

### 58. Letters in Sequence

F, as it is not a vowel.

### 59. 24 H in a D

a) 12 months in a year

b) 7 Wonders of the World

c) 64 Squares on a Chess Board

d) 26 letters of the alphabet

### 60. Dots

B is correct.

### 61. Dots 2

D is correct, as the dots are rotating clockwise.

## Lateral Thinking Problems

### 62. Classic: Didn't Drown

He fell into the Dead Sea, where water is salty and dense that anyone in it floats very easily.

### 63. What am I?

A Candle.

### 64. Right Hand

Your right elbow and forearm.

### 65. Classic: Six Eggs

The last person took the basket with the last egg still inside.

### 66. Who is Behind Who?

Amy and Tina are standing back to back.

### 67. Classic: Condemned

The third. Lions that haven't eaten in three years are dead.

### 68. Classic: Three Switches and Three Bulbs

Switch one light on for a minute; turn it off and turn another on. Go inside the room and feel the off-bulbs. The warm one is connected to the first switch, the bulb that is on, is connected to the second switch.

## Visual Spatial Intelligence

### 69. Four Sided Figures

There are 25 four sided figures in the diagram.

### 70. Classic: Hermann Grid

There are only two colors in the grid, but what has happened is that the high contrast black and white areas trick the eyes into seeing a grey circle at each intersection.

### 71. Shape Together

C is correct.

### 72. Rubik's cube

**A** is the answer.

### 73. Figure series

A is correct.

### 74. Spatial Reasoning

**C**.

### 75. 16 Circles

### 76. How Many Triangles

27 triangles can be found.

### 77. Change Direction

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If that's your method for 36, your answer is incorrect.

FDO

CBC

ECH

BG?

(F-1)(D-1)=O, because (6-1)(4-1)=5*3=15=O

BUT

(C-1)(B-1)≠C, because C=3, B=2, (3-1)(2-1)=2*1=2≠(3=C)

(E-1)(C-1)=H, because (5-1)(3-1)=4*2=8=H,

therefore

(B-1)(G-1)=F, because B=2, G=7, (2-1)(7-1)=1*6=6=F, not G.

Also, did you flip your answers for 71 and 72? The Rubik's cube answer can be proven incorrect simply by acknowledging which colours show themselves after each flip of the box. Green is on the back left while grey is on the bottom, and so C would reveal the one side of the cube which hasn't been flipped yet, not A, which actually starts to multiply the number of yellows that exist on the cube.

Not to mention I really see no way whatsoever in which the two shapes in 71 can combine to form C, and if that really is your answer I would sure like to an explanation.

You're absolutely right, I had accidentally written the answers in 71 and 72 in a wrong order, and 36 was incorrect. The answer should be F, I must have taken away 1 there as well. I have changed it now

Thank you for the corrections Ryan.

I think you forgot to correct the order of the answers in 71 and 72...

I think, we can choose B for number 22

ATRUNE = Nature

answer to 12. shouldn't be 65535? (257 * 255)

@ay You are totally right. Another solution is (2^2^i) - 1 where i is incremented every time and i starts at 0.

(2^2^0) - 1 = 1

(2^2^1) - 1 = 3

(2^2^2) - 1 = 15

(2^2^3) - 1 = 255

(2^2^4) - 1 = 65535