My Neurons Love Me For Exercising Them
Last Problem:
In a class of 20 boys, 14 have blue eyes, 12 have black hair, 11 are overweight (this is 2010 after all) and 10 are tall.
How many boys in the class are tall, overweight, black haired and blue eyed?
Answer:
There can conceivably be as many as 10 such boys or as few as one.
Today’s Problem:
Betty is a dog walker. She has six dogs to walk every day. If Betty walks two dogs at a time [after all – there is only one of her] how many different pairs of dogs can she take out for a walk?
Last Problem:
If seven horses have entered a race, how many different ways can the first three places (first place, second place and third place) be filled?
Answer:
210
For whichever of the seven horses comes in first, there are six different horses that can come in second; for each of the 42 combinations of first and second place horses [7 x 6)], there are five horses can can come in third. This means in effect that there are 7 x 6 x 5 = 210 different combinations of horses that can come in first, second or third place in the race.
Today’s Problem:
In a class of 20 boys, 14 have blue eyes, 12 have black hair, 11 are overweight (this is 2010 after all) and 10 are tall.
How many boys in the class are tall, overweight, black haired and blue eyed?
Last Problem:
A telephone cable has 20 wires – five in each of four different colors: red, yellow, green and blue. If you are working in total darkness, how many wires must you grab to ensure that you have at least one of each color?
Answer:
To take into account the worst possible scenario, you would have to grab sixteen wires : (For example. five red, five yellow, five green and one blue).
Today’s Problem:
If seven horses have entered a race, how many different ways can the first three places (first place, second place and third place) be filled?
Last Problem:
A bathtub holding an iceberg is filled to the brim with water. Some of the iceberg floats above the water line. Most of it is under the water. What will happen when the iceberg melts? Will the water spill onto the bathroom floor and make a huge mess?
Answer:
The water level will stay exactly as before.
The weight of the water displaced by the iceberg exactly equals the weight of the iceberg. When the iceberg melts, it turns back into water and fills the volume of water that it displaced.
The volume of the iceberg above the water must exactly equal the increased volume of the water that froze and expanded to become ice.
Today’s Problem:
A telephone cable has 20 wires – five in each of four different colors: red, yellow, green and blue, If you are working in total darkness, how many wires must you grab to ensure that you have at least one of each color?
Yesterday’s Problem:
Place a mirror in front of the two paragraphs below. Words in the top frame will appear reversed right to left as you would expect. But, words in the bottom frame will appear upside-down. What’s up here? Why does this happen?
PLACE A MIRROR VERTICALLY
ON THE LEFT RED.
WORDS IN THE TOP FRAME
WILL BE REVERSED RIGHT-LEFT
(BUT NOT UPSIDE DOWN). WORDS
AT THE BOTTOM FRAME ARE NOT
ONLY REVERSED, BUT ALSO
TURNED UPSIDE-DOWN. CAN
YOU EXPLAIN WHY?
BOOKIE EXCEEDED HIKED
ICEBOX CHOKED COED
BOBBED DECK BEECED COD
HID BOXED DODO BOB
CHOKED COCO EXCEEDED
BOOKIE HIKED ICEBOX DID
CHOICE BOOKED OBOE
HEEDED OX HID COKE
EXHOED BOOHOO DOCKED
Answer:
Letters in the words found in the bottom frame all have horizontal symmetry. For such an image, a reflection is the same as a 180 degree rotation. The rotation is more easily perceived because the image still spells out recognizable English words.
Today’s Problem:
A bathtub holding an iceberg is filled to the brim with water. Some of the iceberg floats above the water line. Most of it is under the water. What will happen when the iceberg melts? Will the water spill onto the bathroom floor and make a huge mess?
Last Problem:
Five identical one pound lead weights are dropped simultaneously into each of five gallon containers that are filled with different substances at the temperatures noted below. In which of the five containers will the weight take the longest to reach the bottom?
Container One: Milk at 50 degrees F
Container Two: Honey at 60 degrees F
Container Three: Water at 20 degrees F
Container Four: Alcohol at 30 degrees F
Container Five: Oil at 40 degrees F
Answer:
Container Three: Why?
Because water is frozen at 20 degrees F.
Today’s Problem:
Place a mirror in front of the two paragraphs below. Words in the top frame will appear reversed right to left as you would expect. But, words in the bottom frame will appear upside-down. What’s up here? Why does this happen?
PLACE A MIRROR VERTICALLY
ON THE LEFT RED.
WORDS IN THE TOP FRAME
WILL BE REVERSED RIGHT-LEFT
(BUT NOT UPSIDE DOWN). WORDS
AT THE BOTTOM FRAME ARE NOT
ONLY REVERSED, BUT ALSO
TURNED UPSIDE-DOWN. CAN
YOU EXPLAIN WHY?
BOOKIE EXCEEDED HIKED
ICEBOX CHOKED COED
BOBBED DECK BEECED COD
HID BOXED DODO BOB
CHOKED COCO EXCEEDED
BOOKIE HIKED ICEBOX DID
CHOICE BOOKED OBOE
HEEDED OX HID COKE
EXHOED BOOHOO DOCKED