Each month, a new set of puzzles will be posted. Come back next month for the solutions and a new set of puzzles, or subscribe to have them sent directly to you.
In the following numeric series: 4, 8, 7, 5, 1, ?, ?, ?; what would be the next three terms (6th, 7th, and 8th ) in the series?
A bag contains 1 dollar, 50 cents and 25 cents coins in the ratio 3 : 5 : 7. The total amount is $1,856. How do you find the number of each denomination?
Replace each letter with a number (i.e. 1 to 9) to make the following equations true.
In these puzzles, each row, column and diagonal is an equation. Use the numbers 1 to 9 to complete the equations and each number can be used only once. ‘One’ number has been provided to get you started. Find the remaining eight numbers that satisfies all the resulting equations. Note: As in normal algebraic operation, multiplication (x) and division (/) are performed before addition (+) and subtraction ().
There are more than one way of doing these puzzles and may well be more than one answer. Please let me and others know what alternatives you find by commenting below. We also welcome general comments on the subject and any feedback you'd like to give.
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Ronald, Tony, Fiona, Paula and John have their birthdays on consecutive days, all between Monday and Friday.
Can you figure out whose birthday is on each day?
Solution:
Monday – John, Tuesday – Tony, Wednesday – Ronald, Thursday – Paula, Friday – Fiona
Four playing cards, one of each suit (spades, clubs, hearts, & diamonds) face down on a table. They are a three, a four, a five, and a six.
Can you determine the cards’ suits and their order?
Solution:
From left to right: 3 of diamonds, 6 of spades, 4 of hearts, and 5 of clubs.
You’ve been invited to a party at Charlie’s house, but you’ve never been there. He has seven friends who live nearby. They’ve given you the following map showing all of their houses including Charlie’s house, along with the following information:
Can you figure out who lives where, and also which house is Charlie’s?
Solution:
On the the map, the friends / neighbours live in the following houses with respect to Charlie’s house:
A – Elena, B – Benita, C – Hal, D – Greta, E – Charlie, F – Daniel, G – Adam, H – Franco
Each month, a new set of puzzles will be posted. Come back next month for the solutions and a new set of puzzles, or subscribe to have them sent directly to you.
Ronald, Tony, Fiona, Paula and John have their birthdays on consecutive days, all between Monday and Friday.
Can you figure out whose birthday is on each day?
Four playing cards, one of each suit (spades, clubs, hearts, & diamonds) face down on a table. They are a three, a four, a five, and a six.
Can you determine the cards’ suits and their order?
You’ve been invited to a party at Charlie’s house, but you’ve never been there. He has seven friends who live nearby. They’ve given you the following map showing all of their houses including Charlie’s house, along with the following information:
Can you figure out who lives where, and also which house is Charlie’s?
There are more than one way of doing these puzzles and may well be more than one answer. Please let me and others know what alternatives you find by commenting below. We also welcome general comments on the subject and any feedback you'd like to give.
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c)
Puzzle OneIn two years time my age will be three times the age of my son was two years ago. Three years ago my age was twice the age of my same son will be in three years time. How old are we both? Solution: Let x = my age and y = my son’s age Given: (x + 2) = 3(y – 2); x + 2 = 3y – 6; x = 3y – 8 and (x – 3) = 2(y + 3); x – 3 = 2y + 6; x = 2y + 9 Combining the two equations for x: 3y – 8 = 2y + 9; 3y – 2y = 9 + 8 Therefore, y = 17 (my son’s age) and x = 3y – 8 or x = 3(17) – 8 = 43 (my age) Verifying results: x = 2y + 9 or x = 2(17) + 9 = 43 
Puzzle TwoThere are 10 points equally spaced around the circle with interconnecting lines drawn between them.
Solution: Note: The following approach for counting the number of lines connecting the dots in a circle cans also be used for the number of individuals in a room shaking the hand with each of the other persons once. a) Each of the 10 dots on the circle connects with 9 of the other dots or 10 x 9 = 90 lines. Since there are 2 points to every line, then the number of actual line is half of 90 or 45 total lines in the diagram. As an alternate approach, physical count them in the diagram. b) If you now have 50 dots on the circle, each will connect with 49 of the other dots or 50 x 49 = 2,450 lines. Since there are 2 points to every line, then the number of actual line is half of 2,450 or 1,225 total lines in the diagram. c) If you now have 100 dots on the circle, each will connect with 99 of the other dots or 100 x 99 = 9,900 lines. Since there are 2 points to every line, then the number of actual line is half of 9,900 or 4,950 total lines in the diagram. 
Puzzle ThreeThe missing numbers are between 0 & 9. The numbers in each row add up to the totals on the right, and the columns add up to the totals along the bottom. The sums of the diagonals are also given. Find the missing numbers? (Note: there may be more than one solution for each of these puzzles.)

Solutions:

Each month, a new set of puzzles will be posted. Come back next month for the solutions and a new set of puzzles, or subscribe to have them sent directly to you.
There are more than one way of doing these puzzles and may well be more than one answer. Please let me and others know what alternatives you find by commenting below. We also welcome general comments on the subject and any feedback you'd like to give.
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The price of an item was increased by 25% and later decreased by 25%, which makes the price of the item $375. What was the original price?
Solution:
Let p = the original price
Then, 1.25 x 0.75 x p = 375
p = £400
If 3/4 is Peter’s salary is equal to 2/4 of Mary’s salary. What is Peter’s salary if Mary’s salary is £120,000?
Solution:
Let: Peter’s Salary = p
Then, ¾ x p = ½ x 120,000
p = 4/3 x 60,000 = £80,000
418 marbles are initially shared among three kids A, B and C. A got half the amount of C’s share which is 3 times B’s share. If A now wins 35 marbles from B and loses 8 marbles to B in a game of marbles how many marbles do each now have?
Answer: A ends up with 141 marbles, B ends up with 84 marbles, and C has 193 marbles
Solution:
Let x = C’s share
Givens:
A’s share = 1/2 of C’s share, so A’s share = x/2
C’s share = x = 3 x B’s share, so B’s share = x/3
418 = A + B + C = x/2 + x/3 + x = (11/6)(x)
Therefore:
x = (418)(6/11) = (38)(6) = 228 (or C’s share)
B’s share = x/3 = 228/3 = 76 marbles
A’s share = x/2 = 228/2 = 114 marbles
A + B + C = 114 + 76 + 228 = 418
If A now wins 35 marbles from C, but loses 8 marbles to B, then
A now has 114 + 35 – 8 = 141 marbles
B now has 76 + 8 = 84 marbles and
C now has 228 – 35 = 193 marbles
Checking answers, A + B + C = 141 + 84 + 193 = 418
There is a threedigit number. The second digit is four times as big as the third digit (no zeros) while the first digit is three less than the second digit. What is the threedigit number?
Answer: 582
Solution:
Let:
x = 1st single digit number
y = 2nd single digit number
z = 3rd single digit number
n = total 3digit number where no two digits are the same or zero.
Given:
a) 100x + 10y + z = n
b) y = 4z
c) x = y – 3
d) z <= 3 (or 0, 1, 2, or 3)
z can = 1 or 2 but not = 0 or 3 because of step b) and y must be a single digit non zero.
If z = 1, then y = 4 from step b) and x = 1 from step c); x & z can not be the same value or 1)
Therefore, z = 2, then y = 8 from step b), x = 5 from step c) and n = 582 per step a).
Each month, a new set of puzzles will be posted. Come back next month for the solutions and a new set of puzzles, or subscribe to have them sent directly to you.
Puzzle OneIn two years time my age will be three times the age of my son was two years ago. Three years ago my age was twice the age of my same son will be in three years time. How old are we both? 
Puzzle TwoThere are 10 points equally spaced around the circle with interconnecting lines drawn between them. 
Puzzle ThreeThe missing numbers are between 0 & 9. The numbers in each row add up to the totals on the right, and the columns add up to the totals along the bottom. The sums of the diagonals are also given. Find the missing numbers? (Note: there may be more than one solution for each of these puzzles.)

There are more than one way of doing these puzzles and may well be more than one answer. Please let me and others know what alternatives you find by commenting below. We also welcome general comments on the subject and any feedback you'd like to give.
If you have a question that needs a response from me or you would like to contact me privately, please use the contact form.
If you've enjoyed doing the puzzles, consider ordering the books;
Both in a handy pocket sized format. Click here for full details.
The price of an item was increased by 25% and later decreased by 25%, which makes the price of the item $375. What was the original price?
Solution:
Let p = the original price
Then, 1.25 x 0.75 x p = 375
p = £400
If 3/4 is Peter’s salary is equal to 2/4 of Mary’s salary. What is Peter’s salary if Mary’s salary is £120,000?
Solution:
Let: Peter’s Salary = p
Then, ¾ x p = ½ x 120,000
p = 4/3 x 60,000 = £80,000
418 marbles are initially shared among three kids A, B and C. A got half the amount of C’s share which is 3 times B’s share. If A now wins 35 marbles from B and loses 8 marbles to B in a game of marbles how many marbles do each now have?
Answer: A ends up with 141 marbles, B ends up with 84 marbles, and C has 193 marbles
Solution:
Let x = C’s share
Givens:
A’s share = 1/2 of C’s share, so A’s share = x/2
C’s share = x = 3 x B’s share, so B’s share = x/3
418 = A + B + C = x/2 + x/3 + x = (11/6)(x)
Therefore:
x = (418)(6/11) = (38)(6) = 228 (or C’s share)
B’s share = x/3 = 228/3 = 76 marbles
A’s share = x/2 = 228/2 = 114 marbles
A + B + C = 114 + 76 + 228 = 418
If A now wins 35 marbles from C, but loses 8 marbles to B, then
A now has 114 + 35 – 8 = 141 marbles
B now has 76 + 8 = 84 marbles and
C now has 228 – 35 = 193 marbles
Checking answers, A + B + C = 141 + 84 + 193 = 418
There is a threedigit number. The second digit is four times as big as the third digit (no zeros) while the first digit is three less than the second digit. What is the threedigit number?
Answer: 582
Solution:
Let:
x = 1st single digit number
y = 2nd single digit number
z = 3rd single digit number
n = total 3digit number where no two digits are the same or zero.
Given:
a) 100x + 10y + z = n
b) y = 4z
c) x = y – 3
d) z <= 3 (or 0, 1, 2, or 3)
z can = 1 or 2 but not = 0 or 3 because of step b) and y must be a single digit non zero.
If z = 1, then y = 4 from step b) and x = 1 from step c); x & z can not be the same value or 1)
Therefore, z = 2, then y = 8 from step b), x = 5 from step c) and n = 582 per step a).
Each month, a new set of puzzles will be posted. Come back next month for the solutions and a new set of puzzles, or subscribe to have them sent directly to you.
After a day at the races, four friends (A, B, C & D), compared their winnings and losses and found that between them they had broken even. D had lost twice as much as B won. B won £10 less than A lost, and A had lost £20 less than C won. How did each of them do?
“And now over to Brian Barber who can tell us what happened.”
“Thank you, Kim. It was truly gripping race with a lot of money on the favourite Don Quay. The four horses jumped the last fence in a bunch with Known Hope in second, but as they ran up to the finish line the leader at the last fence faded to third place. Also Ran improved one place from the last hedge to the finish line and Always True brought up the rear.”
What was the order over the last fence and at the finished line?
Write the numbers 1, 3, 5, 7, 9, 11 and 13 in the circles so that each line of three numbers adds up to 21.
There are more than one way of doing these puzzles and may well be more than one answer. Please let me and others know what alternatives you find by commenting below. We also welcome general comments on the subject and any feedback you'd like to give.
If you have a question that needs a response from me or you would like to contact me privately, please use the contact form.
If you've enjoyed doing the puzzles, consider ordering the books;
Both in a handy pocket sized format. Click here for full details.
The price of an item was increased by 25% and later decreased by 25%, which makes the price of the item $375. What was the original price?
Solution:
Let p = the original price
Then, 1.25 x 0.75 x p = 375
p = £400
If 3/4 is Peter’s salary is equal to 2/4 of Mary’s salary. What is Peter’s salary if Mary’s salary is £120,000?
Solution:
Let: Peter’s Salary = p
Then, ¾ x p = ½ x 120,000
p = 4/3 x 60,000 = £80,000
418 marbles are initially shared among three kids A, B and C. A got half the amount of C’s share which is 3 times B’s share. If A now wins 35 marbles from B and loses 8 marbles to B in a game of marbles how many marbles do each now have?
Answer: A ends up with 141 marbles, B ends up with 84 marbles, and C has 193 marbles
Solution:
Let x = C’s share
Givens:
A’s share = 1/2 of C’s share, so A’s share = x/2
C’s share = x = 3 x B’s share, so B’s share = x/3
418 = A + B + C = x/2 + x/3 + x = (11/6)(x)
Therefore:
x = (418)(6/11) = (38)(6) = 228 (or C’s share)
B’s share = x/3 = 228/3 = 76 marbles
A’s share = x/2 = 228/2 = 114 marbles
A + B + C = 114 + 76 + 228 = 418
If A now wins 35 marbles from C, but loses 8 marbles to B, then
A now has 114 + 35 – 8 = 141 marbles
B now has 76 + 8 = 84 marbles and
C now has 228 – 35 = 193 marbles
Checking answers, A + B + C = 141 + 84 + 193 = 418
There is a threedigit number. The second digit is four times as big as the third digit (no zeros) while the first digit is three less than the second digit. What is the threedigit number?
Answer: 582
Solution:
Let:
x = 1st single digit number
y = 2nd single digit number
z = 3rd single digit number
n = total 3digit number where no two digits are the same or zero.
Given:
a) 100x + 10y + z = n
b) y = 4z
c) x = y – 3
d) z <= 3 (or 0, 1, 2, or 3)
z can = 1 or 2 but not = 0 or 3 because of step b) and y must be a single digit non zero.
If z = 1, then y = 4 from step b) and x = 1 from step c); x & z can not be the same value or 1)
Therefore, z = 2, then y = 8 from step b), x = 5 from step c) and n = 582 per step a).
Each month, a new set of puzzles will be posted. Come back next month for the solutions and a new set of puzzles, or subscribe to have them sent directly to you.
The price of an item was increased by 25% and later decreased by 25%, which makes the price of the item $375. What was the original price?
If 3/4 is Peter’s salary is equal to 2/4 of Mary’s salary. What is Peter’s salary if Mary’s salary is £120,000?
418 marbles are initially shared among three kids A, B and C. A got half the amount of C’s share which is 3 times B’s share. If A now wins 35 marbles from B and loses 8 marbles to B in a game of marbles how many marbles do each now have?
There is a threedigit number. The second digit is four times as big as the third digit (no zeros) while the first digit is three less than the second digit. What is the threedigit number?
There are more than one way of doing these puzzles and may well be more than one answer. Please let me and others know what alternatives you find by commenting below. We also welcome general comments on the subject and any feedback you'd like to give.
If you have a question that needs a response from me or you would like to contact me privately, please use the contact form.
If you've enjoyed doing the puzzles, consider ordering the books;
Both in a handy pocket sized format. Click here for full details.
Go to START and proceed through this numeric maze, following instructions until you get to the FINISH box. What number did you finish with? 
Each month, a new set of puzzles will be posted. Come back next month for the solutions and a new set of puzzles, or subscribe to have them sent directly to you.
Go to START and proceed through this numeric maze, following instructions until you get to the FINISH box. What number did you finish with? 
There are more than one way of doing these puzzles and may well be more than one answer. Please let me and others know what alternatives you find by commenting below. We also welcome general comments on the subject and any feedback you'd like to give.
If you have a question that needs a response from me or you would like to contact me privately, please use the contact form.
If you've enjoyed doing the puzzles, consider ordering the books;
Both in a handy pocket sized format. Click here for full details.
What number should be subtracted from 13/12 to get 12/13?
Solution:
Let n = number needed
(13/12 – n) = 12/13
12(13/12 – n) = 12(12/13)
13 – 12n = 144/13
12n = 144/13 – 13(13/13) =
– 12n =144/13 – 169/13) = 25/13
n = 25 / (13*12)
n = 25/156
Checking: (13/12) – (25/156) = (169/156) – (25/156) = 144/156 =12/13
Container A holds 5 times as much milk as Container B. After 1.25 litres of milk from Container A is poured into Container B, both containers have the same amount of milk. How much milk did each container hold at first?
Solution:
Let container B contain x litres of milk
Then, container A contains 5x litres of milk
After 1.25 litres of milk from container A is poured into container B, both containers have the same amount of milk or
(5x – 1.25) = (x + 1.25); 4x = 2.5; x = 0.625 litres
Therefore at first, container B had 0.625 litres of milk and
container A had 0.625 x 5 = 3.125 litres of milk.
There are some people on a boat. 48 get off the boat at the first stop. 62 people get on the second stop and half that is on the boat got off at the third stop. Now there are 73 people on the boat. How many people were on the boat prior to the first stop?
Solution:
Let x = number of people on the boat prior to its 1st stop.
Then, (on prior to 1st stop) – (off after 1st stop) + (on at 2nd stop) – (off after 3rd stop) = (on after 3rd stop)
Therefore, x – 48 + 62 – ½ (x – 48 + 62) = 73
x – 48 + 62 – ½ x + 24 – 31 = 73
½ x = 73 + 48 – 62 – 24 + 31 = 66
x = 66 * 2 = 132 people on the boat prior to the first stop.
King Tut died 120 years after King Eros was born. Their combined ages when they died was 100 years. King Eros died in the year 40 B.C. In what year was King Tut born?
Answer:
King Tut was born in 20 B.C.
Solution:
There were 120 years between the birth of King Eros and the death of King Tut, but since their combined ages amounted to only 100 year, there must have been 20 years (120 – 100) when King Tut did not exist. This would be a period between the death of King Eros, 40 B.C., and the birth of King Tut, year 20 B.C.
Each month, a new set of puzzles will be posted. Come back next month for the solutions and a new set of puzzles, or subscribe to have them sent directly to you.
What number should be subtracted from 13/12 to get 12/13?
Container A holds 5 times as much milk as Container B. After 1.25 litres of milk from Container A is poured into Container B, both containers have the same amount of milk. How much milk did each container hold at first?
There are some people on a boat. 48 get off the boat at the first stop. 62 people get on the second stop and half that is on the boat got off at the third stop. Now there are 73 people on the boat. How many people were on the boat prior to the first stop?
King Tut died 120 years after King Eros was born. Their combined ages when they died was 100 years. King Eros died in the year 40 B.C. In what year was King Tut born?
There are more than one way of doing these puzzles and may well be more than one answer. Please let me and others know what alternatives you find by commenting below. We also welcome general comments on the subject and any feedback you'd like to give.
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If you've enjoyed doing the puzzles, consider ordering the books;
Both in a handy pocket sized format. Click here for full details.
How many 3digit numbers are divisible by 7?
Solution:
The largest 2digit and 3digit numbers divisible by 7 are:
98 = 14 x 7 and 994 = 142 x 7.
There are therefore, including zero, 15 1 and 2digit numbers divisible by 7, and
143 1, 2 and 3digit numbers divisible by 7.
Thus, 143 – 15 = 128 3digit numbers divisible by 7.
In a certain class, 60% of the students are female and 40% are male. If 80% of the females and 50% of the males get A grades, what percentage of the class gets an A?
Solution:
Suppose there are n students in the class. Then there are 0.60 x n females and 0.40 x n males in the class.
(0.80 x 0.60) x n = 0.48 x n females & (0.70 x 0.40) x n = 0.28 x n males get an A.
Therefore, (0.48 + 0.28) x n =.0.76 x n, or 76%, of the class get an A.
A certain number of persons are standing in a row. Jake is18th from the left end and Tiny is 23rd from the right end. If they interchange their positions, Tiny becomes 33rd from the right end. How many persons are in the row?
Solution:
Therefore, the number of persons in the row = 18 + 33 – 1 (Jake included twice) = 50
A ship is sailing north at a speed of 20 km/hour. A second ship directly south of this is sailing east at a speed of 15 km/h. How fast are they travelling apart?
Solution:
Each hour the ships will have increased their South North separation by 20 km and their West East separation by 15 km.
Using Pythagorean Theorem for right triangles (a² + b² = c²):
Thus, the ships will have an increased separation of
√(202 + 152) = √625 = 25 km.
The ships are, therefore, travelling apart at a rate of 25 km/h
Each month, a new set of puzzles will be posted. Come back next month for the solutions and a new set of puzzles, or subscribe to have them sent directly to you.
How many 3digit numbers are divisible by 7?
In a certain class, 60% of the students are female and 40% are male. If 80% of the females and 70% of the males get A grades, what percentage of the class gets an A?
Certain number of persons are standing in a row. Jake is 18th from the left end and Tiny is 23rd from the right end. If they interchange their positions, Tiny becomes 33rd from the right end. How many persons are there in the row?
A ship is sailing north at a speed of 20 km/hour. A second ship directly south of this is sailing east at a speed of 15 km/hour. How fast are they traveling apart?
There are more than one way of doing these puzzles and may well be more than one answer. Please let me and others know what alternatives you find by commenting below. We also welcome general comments on the subject and any feedback you'd like to give.
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Two trains are heading towards each other on parallel tracks The first train is traveling at 60 mph and the second train is traveling at 40 mph. The distance between the two trains is 500 miles. If they started at the same time, how long will it take before they begin to pass each other?
Solution:
The trains are approaching each other at 100 mph, so will take 5 hours to cover the 500 miles.
If the third term of an arithmetic sequence is 15 and the eighth term is 40, what is the 20th term?
Solution:
15/3 = 5, 40/8 = 5; therefore, 20 * 5 = 100
The sum of two numbers is 25. If three times the first number is subtracted from twice the second number, the result is 7. What are the two numbers?
Solution:
If the 1st number is x and the second number is y, then
x + y = 25; y = 25 – x
2y – 3x = 7; 2(25 – x) – 3x = 7
Therefore, 50 – 2x – 3x = 7; 5x = 43
So, x = 8.6 and y = 25 – 8.6 = 16.4
Find the numerical equivalent for the following alphameric expressions to satisfy the equations below:
a) XYZ + XZY = ZYX, Solution: 459 + 495 = 954
b) EAT + THAT = APPLE, Solution: 419 + 9619 = 10038
Each month, a new set of puzzles will be posted. Come back next month for the solutions and a new set of puzzles, or subscribe to have them sent directly to you.
Two trains are heading toward each other. The first train is traveling at 60 mph and the second train is traveling at 40 mph. The distance between the two trains is 500 miles. If they started at the same time, how long will it take before they collide?
If the third term of an arithmetic sequence is 15 and the eighth term is 40, what is the 20th term?
The sum of two numbers is 25. If three times the first number is subtracted from twice the second number, the result is 7. What are the two numbers?
Find the numerical equivalent for the following alphameric expressions to satisfy the equations below:
There are more than one way of doing these puzzles and may well be more than one answer. Please let me and others know what alternatives you find by commenting below. We also welcome general comments on the subject and any feedback you'd like to give.
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Six tigers can catch just six rabbits in six minutes. So how many tigers will be needed to catch sixty rabbits in sixty minutes?
Solution: 1 tiger can catch 1 rabbit in 6 minutes. Then in 60 minutes, each tiger can catch 10 rabbits. Then, if this is so, 6 tigers can catch 60 rabbits in 60 minutes.
A wizard was on the way to his house and a few drops from his magic potion fell on to a plant. Now, the plant will double its size every day. It is growing in a circular pond with a circumference of 600 meters. The plantcovered half the pond in 28 days, how many days would it take to cover the full pond?
Solution: If the plant doubles in size every day and the plant covers half the pond in 28 days, then it would completely cover the full pond in 29 days.
If 1=5,
2=25,
3=325,
4=4325,
5=?
Solution: You might immediately think the answer might be 54325. However, the answer is 1. The first line is 1=5 and that means 5 is also equal to one.
Take your favourite number, add this number to itself, then multiply the sum by 4, and finally divide the results by the sum of 3 and 5. What number do you finally get and why?
Solution: Assume your favourite number is 123. Then, (123 + 123) x 4 / (3 + 5) = 123
Why, any number x 8/8 = same number