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 board shown below has 32 cells, one of which is labelled S (Start) and another F (Finish). The shortest path starting at S and finishing at F involves exactly nine other cells and ten moves, where each move goes from cell to cell ‘horizontally’ or ‘vertically’ across an edge.
From S, there are two starting paths:  
We can represent the number of paths to a particular square like this:  
There is only one way to travel along the edges and we can build up our diagram like this, noticing that each square not on an edge can only be reached from the left or from below. 

How many possible paths are there from S to F by using the instructions above? 
There are three circles with centre points A, B and C. Each circle touches the other two circles, and each centre lies outside the other two circles. The sides of the triangle, drawn connecting the 3 points, have lengths 13 cm, 16 cm and 20 cm. What are the radii of each of the three circles?
A large square is split into four congruent squares, two of which are shaded. The other two squares have smaller shaded squares drawn in them whose vertices are the midpoints of the sides of the unshaded squares. What percentage of the diagram is shaded?
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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Four men are throwing darts at a garage door. Their first names are Andy, Brian, Carl and Danny, and their last names (not in the same order) are Anderson, Brown, Clinton, and Dickson. Their ages (not in the same order) are 31, 32, 33 and 34 and each man has one dart. The colours of the four darts (again not in the same order) are Blue, Red, Green, and White.
Danny’s dart sits a little to the right of the Red dart, 72 cm from Brown’s dart, and a little under Andy’s dart. Dickson’s dart sits a little right under the Red dart. Andy’s dart is 97 cm from Dickson’s dart.
Brian is the youngest and the one with the Red dart is older than Clinton, being 2 years younger than the White dart, who again is older than Carl.
For the four men, can you determine what their last names, ages and dart colours are? Also, the distance between the Green and Blue darts?
Solution:
If Alex ate 1/2 of the plate of cookies he found on the counter, then his sister Lucy ate 1/3 of what was left, and then Charley ate 1/2 of those that were left, when their Mum came home and found 2 cookies, how many did the kids eat?
Solution:
Working backward:
As a check, 12/2 = 6, 6/3*2 = 4, 4/2 = 2 cookies
The ration of two numbers is 7:10 and their difference is 105. What are the numbers?
Solution:
Given: The difference between numbers is 105 and the difference between ratio of numbers is 3.
Divide 105 by 3 = 35
Multiply both terms of the ratio by 35 gets the numbers
(35 * 10) – (35 * 7) = 350 – 245 = 105
Therefore, the numbers are 245 and 350.
Jack and Jill went up the hill to fetch a pail of water. They started at the same time, but Jack arrived at the top a half of an hour before Jill. On the way down, Jill calculated that if she had walked 50% faster and Jack had walked 50% slower, then they would have arrived at the top of the hill at the same time. How long did Jill take to walk up to the top of the hill?
Solution:
Let t equal the number of hours that Jill took to walk to the top of the hill.
So the time taken by Jack was (t – ½ ) hours. If Jack had walked 50% more slowly, he would have taken twice as long, i.e., 2(t – ½) = (2t – 1) hours.
If Jill had walked 50% faster, she would have taken 3/2 t hours.
Therefore, with Jack’s 50% slower equalling Jill’s 50% faster
2t – 1 = 3/2 t
1/2 t = 1
t = 2
As a check: (2t – 1) must = (3/2 t) or (2 * 2) – 1 = 3/2 * 2 and thus 3 equals 3.
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.
Four men are throwing darts at a garage door. Their first names are Andy, Brian, Carl and Danny, and their last names (not in the same order) are Anderson, Brown, Clinton, and Dickson. Their ages (not in the same order) are 31, 32, 33 and 34 and each man has one dart. The colours of the four darts (again not in the same order) are Blue, Red, Green, and White.
Danny’s dart sits a little to the right of the Red dart, 72 cm from Brown’s dart, and a little under Andy’s dart. Dickson’s dart sits a little right under the Red dart. Andy’s dart is 97 cm from Dickson’s dart.
Brian is the youngest and the one with the Red dart is older than Clinton, being 2 years younger than the White dart, who again is older than Carl.
For the four men, can you determine what their last names, ages and dart colours are? Also, the distance between the Green and Blue darts?
First name  
Last name  
Age  
Dart colour 
If Alex ate 1/2 of the plate of cookies he found on the counter, then his sister Lucy ate 1/3 of what was left, and then Charley ate 1/2 of those that were left, when their Mum came home and found 2 cookies how many did kids eat?
The ration of two numbers is 7:10 and their difference is 105. What are the numbers?
Jack and Jill went up the hill to fetch a pail of water. They started at the same time, but Jack arrived at the top a half of an hour before Jill. On the way down, Jill calculated that if she had walked 50% faster and Jack had walked 50% slower, then they would have arrived at the top of the hill at the same time. How long did Jill take to walk up to the top of the hill?
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.
A magic rectangular cloth always shrinks its length to 1/2 and width to 1/3 whenever its owner wishes something. After three such wishes, its surface is now 4cm^{2}.
What was the original length if the original width was 9cm?
Solution:
Let x = original width
Starting with the length from the 3rd wish (1.50 cm) and doubling up to the original length where x = 12cm.
Area  
Length (L)  Width (W)  L * W  L  
Initial  x  9  12  
1st wish  0.50 x  6  6  
2nd wish  0.25 x  4  3  
3rd wisg  0.125 x  2.667  4  1.5 
A bag containing coins of 1 dollar, 50 cents and 25 cents in the ratio 3 : 5 : 7. The total amount is $1,856.00. Find the number of coins for each denomination.
Solution:
Let x = total number of coins
Then, (3/15 * x * 1.00) + (5/15 * x * 0.50) + (7/15 * x * 0.25) = 1856.00
Multiplying both sides of equation by 15
3.00x + 2.50x + 1.75x = 1856 * 15
7.25x = 27840
x = 3840
Therefore,
3/15 * 3840 = 768 = number of dollars
5/15 * 3840 = 1280 = number of 50 cent coins
7/15 * 3840 = 1792 = number of 25 cent coins
To check: 768 * 1.00 = 768.00, 1280 * 0.50 = 640.00 and 1792 * 0.25 = 448.00
Therefore, $768 + $640 + $448 = $1,856.00
Below is an special safe’s keypad . To open, you must press the keys in the correct sequencer until the last key marked ‘OPEN’. The number on each key tells you how many keys that you must move and the letter tells you in which direction to move (U = up, D = down, L = left and R = right). Which key is the first key in the sequence that you must press to open the safe?
Solution:
The 1^{st} key, to start the sequence to open the safe, is 1L (4^{th} row, 2^{nd} column).
This can be determined by working backward from the final/OPEN key in a reverse direction to the beginning or start/1^{st} key. All keys should b used. Check your start/1^{st} key to see if it starts the sequence to open the safe.
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.
A magic rectangular cloth always shrinks its length to 1/2 and width to 1/3 whenever its owner wishes something. After three such wishes, its surface is now 4cm^{2}.
What was the original length if the original width was 9cm?
A bag containing coins of 1 dollar, 50 cents and 25 cents in the ratio 3 : 5 : 7. The total amount is $1,856.00. Find the number of coins for each denomination.
Below is an special safe’s keypad . To open, you must press the keys in the correct sequencer until the last key marked ‘OPEN’. The number on each key tells you how many keys that you must move and the letter tells you in which direction to move (U = up, D = down, L = left and R = right). Which key is the first key in the sequence that you must press to open the safe?
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.
In the following equations, the value of each of the playing cards (clubs, diamonds, spades, and hearts) will make each equation true. The value of the cards can only be 1 to 10. Find their values.
Solution:
In the following numeric series: 8, 20, 64, 260, ?. What would be the next number (5th) in the series?
Solution:
On the second term, multiply the first term by 3 and then add 4 to the product. All follow on terms, multiple the previous term by one more then the previous term and continue to add 4.
1st term: 8
2nd term: (8*2)+4 = 20
3rd term: (20*3)+4 = 64
4th term: (64*4)+4 = 260
5th term: (260*5)+4 = 1304
The total weight of a tin and the cookies it contains is 2 pounds. After ¾ of the cookies are eaten, the tin and the remaining cookies weigh 0.8 pounds. What is the weight of the tin in pounds?
Solution:
Let the weight of the empty tin = w, and
One quarter of the biscuits weigh ¼ (2 – w)
Then, one quarter of the biscuits + the tin = 0.8 pound = w + (2 – w)/4 and multiplying both sides by 4,
Therefore,: 3.2 = 4w + (2 – w); 3w = 3.2 – 2 = 1.2; w = 0.4 pounds
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 equations, the value of each of the playing cards (clubs, diamonds, spades, and hearts) will make each equation true. The value of the cards can only be 1 to 10. Find their values.
In the following numeric series: 8, 20, 64, 260, ?. What would be the next number (5th) in the series?
The total weight of a tin and the cookies it contains is 2 pounds. After ¾ of the cookies are eaten, the tin and the remaining cookies weigh 0.8 pounds. What is the weight of the tin in pounds?
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.
In the following numeric series: 4, 8, 7, 5, 1, ?, ?, ?; what would be the next three terms (6th, 7th, and 8th ) in the series?
Solution: 4, 8, 7, 5,1, 2, 4, 8
Using the powers of ‘ 2 ‘ plus continually summing their digits until you get a single digit.
2^2 = 4
2^3 = 8
2^4 = 16, 1+ 6 = 7
2^5 = 32, 3+2 = 5
2^6 = 64, 6+4 = 10, 1+0 = 1
6th term: 2^7 = 128, 1+2+8 = 11, 1+1 = 2
7th term: 2^8 = 256, 2+5+6 = 13, 1+3 = 4
Finally, 8th term: 2^9 = 512, 5+1+2 = 8
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?
Solution: 768, 1280 and 1792
Given: Total coins = 3 + 5 + 7 = 15 and total amount = $1,856
Let x = total number of coins
Then, (3x/15 * 1.00) + (5x/15 * 0.50) + (7x/15 * 0.25) = 1856
3.00x + 2.50x + 1.75x = 1856 * 15
7.25x = 27840
x = 3840
Therefore,
3/15 * 3840 = 768 = number of dollar coins
5/15 * 3840 = 1280 = number of 50 cent coins
7/15 * 3840 = 1792 = number of 25 cent coins
To check the results: 768 * 1.00 = 768.00, 1280 * 0.50 = 640.00 and 1792 * 0.25 = 448.00
Therefore,
$768 + $640 + $448 = $1,856.00
Replace each letter with a number (i.e. 1 to 9) to make the following equations true.
Solution:
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 ().
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.
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.
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.
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.
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).
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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?
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Go to START and proceed through this numeric maze, following instructions until you get to the FINISH box. What number did you finish with? 