Posted in Logical, Mathematical on October 26th, 2006 No Comments »
A large toy bag contains 8 yellow Lego pieces, 7 red pieces, and 5 black pieces. Without taking a peek in the bag, Igor takes out N marbles at one. If he is to be sure that he will have 4 Legos of one color and 3 of another left in the bag, what is largest possible value of N?
Update: Solutions are posted!
Posted in Logical, Mathematical on October 26th, 2006 3 Comments »
Here’s a puzzle involving a fair amount of analysis and calculation, but I rather enjoyed doing it.
Allen and Percy were helping their good-tempered teacher Ms. Letourneau move to a new house. There were 16 small boxes and 10 large boxes. Allen takes 2 minutes to move each small box and 6 minutes to move each large box while Percy takes 3 minutes to move each small box and 5 minutes to move each large box. They start moving after school at 4:00pm, and spent 30 minutes to discuss the best strategy to spend the least time moving boxes before getting to work. When is the earliest time they could finish?
Note: They can’t hand off the boxes in the middle of the trip.
Update: Solutions are posted!
Posted in Mathematical on October 26th, 2006 1 Comment »
“Perhaps this will soon turn out to be a blessing, we’ll see,” said the man.
After a few months, his animal came back, leading a fine horse from the north. Everyone congratulated him.
“Perhaps this will soon turn out to be a cause of misfortune, we’ll see,” said the man.
Since he was well-off and kept good horses, his son became fond of riding and eventually broke his thigh bone falling from the very horse from the north and was never able to walk freely. Everyone commiserated with him.
“Perhaps this will soon turn out to be a blessing, we’ll see,” said the man.
One year later, the northern tribes started a big invasion of the border regions.
What blessing do you suppose came from the son breaking his leg?
Posted in Mathematical on October 26th, 2006 1 Comment »
The numbers 182 and 322 can be expressed as the sum of product pairs chosen from the numbers 1 to 12.
182 = 1×12 + 2×11 + 3×10 + 4×9 + 5×8 + 6×7
322 = 1×2 + 3×4 + 5×6 + 7×8 + 9×10 + 11×12
Can the numbers 180, 217, 299, 400 be written the same way?
Posted in Mathematical on October 26th, 2006 No Comments »
Car 1 started from Point A towards point B. At the same time Car 2 started from point B towards A. They crossed each other at point C. After which, Car 1 reached point B in another 9 hrs, and Car 2 reached point A in another 4 hrs. If both the cars maintained a constant speed throughout the journey, and the speed of Car 1 was 36 miles/hr(mph), then what was the speed of Car 2?
Posted in Classic, Mathematical, Paradox on October 24th, 2006 2 Comments »
Posted in Crytarithms, Mathematical on October 23rd, 2006 No Comments »
Since this is quite a tough problem, I’m not going to post nine more problems today, and I hope everyone try this because it is actually really interesting.
Replace the letters and asterisks with digits to satisfy the multiplication:
Don’t ask me what “Estmodus Inrebus” means. I have no clue. FYI this puzzle comes from “The Master Book of Mathematical Recreations” created by a mathematician by the name of Fred Schuh. I’ll try to post a full solution to this problem in a few days.
Edit: I just found out what the phrase means. It’s actually “Est modus in rebus”, a quote from Horace (Ancient Roman poet), meaning “There is a measure in things”.
Update: The complete solution is posted!
Posted in Mathematical on October 22nd, 2006 No Comments »
Posted in Mathematical on October 19th, 2006 No Comments »
How do you place the digits 0~7 on the corners of a cube such that the sums of all sets of two numbers sharing a common edge are prime?
Update: Solutions are posted!
Posted in Classic, Logical, Mathematical on October 17th, 2006 No Comments »
Abe, Bonnie, Cane and Daria have a two-person boat and can cross the river in 5, 10, 20 and 25 minutes respectively. If a boat containing two people can go only as fast as the slower person, how can all four cross the river in one hour?
Update: Solutions are posted.
Posted in Mathematical on October 17th, 2006 No Comments »
What’s the area of the triangle whose three sides and height are four consecutive numbers?
Update: Solutions are posted.
Posted in Mathematical on October 17th, 2006 No Comments »
At what time between three and four oclock will be the minute hand be as far from twelve on the left side of the dial plate as the hour hand is from twelve on the right side of the dial plate?
Source: 536 Problems & Curious Puzzles by Dudeney (p. 15)
Update: Solutions are posted.
Posted in Mathematical on October 17th, 2006 No Comments »
Posted in Mathematical on October 8th, 2006 1 Comment »
Folks, we’re undergoing some technical issues at the moment (including looking for a hosting company), so for a week or so we’re going to have a reduced number of problems each day. Thanks so much for your patience!
What number added to 100 and 164 (separately) is a perfect square number?
Update: Solutions are posted!
Posted in Mathematical on October 8th, 2006 No Comments »
The clerks attached to the firm of Pilkins and Popinjay arranged that three of them would lunch together every day at a particular table so long as they could avoid the same three men sitting down twice together. The same number of clerks of Messrs. Radson, Robson and Ross decided to do precisely the same, only with four men at a time instead of three. On working it out they found that Radson’s staff could keep it up exactly three times as many days as their neighbors. What is the least number of men there could have been in each staff?
Source: 536 Puzzles & Curious Problems by Dudeney (p.175)
Update: Solutions are posted!
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