DAY 422
What is the most recent year that contains all even digits, before the year 2000?
Answer:
Since all digits must be even, it cannot be in the previous millennium. So it must be 888.
Tuesday, 5 August 2014
Sunday, 15 June 2014
DAY 421
HEADS OR TAILS
You are in a dark room and have 100 coins spread out in front of you. Ninety are facing heads up and ten are facing tails up. The coins are mixed up, and you cannot see which way they are facing. How can you sort the coins into two piles, such that each pile has the same number of coins facing tails up?
Answer:
Since the piles don't need to be the same size, make one pile of ten coins and one pile of the other ninety. Flip all of the coins in the pile of ten, and now both piles will have the same number of coins facing tails up.
Example:
Suppose you have three coins facing tails up in the pile of ten. This means there are seven coins facing tails up in the pile of ninety. If you flip all ten coins in the ten pile, you now have seven coins facing tails up - just as in the pile of ninety.
HEADS OR TAILS
You are in a dark room and have 100 coins spread out in front of you. Ninety are facing heads up and ten are facing tails up. The coins are mixed up, and you cannot see which way they are facing. How can you sort the coins into two piles, such that each pile has the same number of coins facing tails up?
Answer:
Since the piles don't need to be the same size, make one pile of ten coins and one pile of the other ninety. Flip all of the coins in the pile of ten, and now both piles will have the same number of coins facing tails up.
Example:
Suppose you have three coins facing tails up in the pile of ten. This means there are seven coins facing tails up in the pile of ninety. If you flip all ten coins in the ten pile, you now have seven coins facing tails up - just as in the pile of ninety.
DAY 420
TWO BLIND MEN
A blind man goes to the mall and buys three pairs of red socks and three pairs of white socks. Another blind man is also at the mall, returning the three pairs of red socks and three pairs of white socks that he bought the day before. The two men bump into each other and all the socks are scattered on the floor, but each pair remains held together by a rubber band. The two blind men are able to gather the six pairs of socks together. Without any help, they are quickly able to sort the socks so that each man ends up with the same number and color of socks he started with - six red and six white. There is no indication on the socks as to their color. How do these two blind men do it?
Answer:
One of the men takes the rubber band off each pair. He keeps one sock for himself and gives the other to the other man.
TWO BLIND MEN
A blind man goes to the mall and buys three pairs of red socks and three pairs of white socks. Another blind man is also at the mall, returning the three pairs of red socks and three pairs of white socks that he bought the day before. The two men bump into each other and all the socks are scattered on the floor, but each pair remains held together by a rubber band. The two blind men are able to gather the six pairs of socks together. Without any help, they are quickly able to sort the socks so that each man ends up with the same number and color of socks he started with - six red and six white. There is no indication on the socks as to their color. How do these two blind men do it?
Answer:
One of the men takes the rubber band off each pair. He keeps one sock for himself and gives the other to the other man.
Monday, 30 December 2013
DAY 419
Together, a hat and scarf cost $11.00. The hat costs $2.00 more than the scarf. What is the price of each?
Answer:
$6.50 for the hat and $4.50 for the scarf.........This counter-intuitive answer can be found by trial and error or algebra [x + (x + 2) = 11]. But a more interesting way to solve the problem is to divide $11.00 in half - $5.50 - and "splitting the difference" of $2.00 by going up $1.00 and down $1.00 - giving $6.50 and $4.50.
NOTE: See also DAY 57 - "bottle and cork" problem
Similar Problem:
Together, soup and a sandwich cost $3.50. A sandwich costs $1.00 more than soup. What is the price of each?
Answer:
$2.25 for the sandwich and $1.25 for the soup
Together, a hat and scarf cost $11.00. The hat costs $2.00 more than the scarf. What is the price of each?
Answer:
$6.50 for the hat and $4.50 for the scarf.........This counter-intuitive answer can be found by trial and error or algebra [x + (x + 2) = 11]. But a more interesting way to solve the problem is to divide $11.00 in half - $5.50 - and "splitting the difference" of $2.00 by going up $1.00 and down $1.00 - giving $6.50 and $4.50.
NOTE: See also DAY 57 - "bottle and cork" problem
Similar Problem:
Together, soup and a sandwich cost $3.50. A sandwich costs $1.00 more than soup. What is the price of each?
Answer:
$2.25 for the sandwich and $1.25 for the soup
Monday, 25 November 2013
Tuesday, 19 November 2013
DAY 417
Fill in the blanks with five different numbers so that the following makes sense when read aloud:
We had been on a losing streak _____ much _____ long. But today we finally _____ a game. To celebrate we _____ _____.
Answer:
We had been on a losing streak 4 much 2 long. But today we finally 1 a game. To celebrate we 8 (Pi).
Credit: GAMES Magazine - April, 2006
R. H. Wei
EASY AS PIE
Fill in the blanks with five different numbers so that the following makes sense when read aloud:
We had been on a losing streak _____ much _____ long. But today we finally _____ a game. To celebrate we _____ _____.
Answer:
We had been on a losing streak 4 much 2 long. But today we finally 1 a game. To celebrate we 8 (Pi).
Credit: GAMES Magazine - April, 2006
R. H. Wei
EASY AS PIE
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