MATH PUZZLES

1]A car travelled from London at a speed of 40mph. Its fuel consumption was 30 mpg. It had a 5 gallon tank which was full when it started, but at that very moment began to leak fuel. After 60 miles the car stopped with a completely empty tank. How many gallons per hour was it losing?

a]2 gallons per hour. The car travelled 60 miles before stopping, this means it used 2 gallons. The car took 1.5 hours to travel 60 miles. Therefore the car lost 3 gallons in 1.5 hours = 2 gallons per hour.



2]In farmer Brown's hay loft there are a number of animals, in particular crows, mice and cockroaches. Being bored one day, I decided to count the animals and found there were exactly 150 feet and 50 heads in total, and there were twice as many cockroaches as mice. How many of each animal were there?

a]10 cockroaches, 5 mice and 35 birds.



3]Our local scrap merchant had to travel to the county recycling plant, 60 miles away. On the way there he could only manage a steady 12mph, fully laden. On the way back, he could manage a steady 16mph. He placed 24 gallons of fuel in the tank ready for the round trip, thinking that this would be enough as the wagon managed to travel 8 miles per gallon. Unfortunately, a piece of metal pierced his fuel pipe at the start of the trip and the wagon started to lose 1 gallon of fuel per hour. Luckily he only lost fuel when moving and he lost no fuel whilst unloading his scrap metal. Were 24 gallons enough for the round trip?

a]Yes, the trip itself used 15 gallons and the wagon lost 8.75 gallons during transit = 23.75 gallons, of the available 24 gallons.


4]Can you find a five digit number which has no zeros no digit is repeated, where:

The first digit is a prime number.
The second digit is the fifth digit minus the first digit.
The third digit is twice the first digit.
The fourth digit is the third digit plus three.
The fifth digit is the difference between the first digit and the fourth digit.


a]23475.



5]A fire engine was rushing to a small fire, 15 miles away. The fire engine set out with 120 gallons of water, however, the water tank had a leak and the fire engine was losing water at the rate of 2 gallons per minute. The fire engine travelled at a constant 30 miles per hour. The fire required 50 gallons of water - did the fire engine have enough water when it arrived?


a]Yes: the journey took 30 minutes. In that time the fire engine lost 60 gallons of water - leaving 60 gallons with which to fight the fire.



6]My local greengrocer is a would-be mathematician. He likes to arrange his apples in nice rows. However, when he lays his apples in rows of 3 he has one left over. When he lays them in rows of 5 he also has one left over. Remarkably he also has one left over when he arranges them in rows of 7 and 9. 11 seems to be the magic number, for, in rows of 11 there are no apples left over. How many apples does the greengrocer have?

a]946.



7]The local river Trent is 4100 inches wide, which happens to be a fantastic number. There is a magnificent, perfectly straight, bridge which spans the river. During a recent survey of the area it was found that one seventh of the overall length of the bridge was on one side of the river and one eighth of the bridge was on the other side of the river. How long is the bridge which spans the river Trent?

a]5600 inches: x/7 + x/8 + 4100 = x, where x is the length of the bridge.


8]A kind old gentleman decided to give 12 sweets to each of the girls in his town and 8 sweets to each of the boys. Of the 612 children in his town, only half the girls and three quarters of the boys were allowed to take the sweets. How many sweets did the kind old gentleman have to buy?

a]3,672. Clue: choose a random number of girls and work it out.



9]Move from letter to letter and collect the necessary letters for DUCK. How many different routes can you take if you always start with the central D and always move either horizontally or vertically?

K
CUK
KCKUK
KUCDUUC
UCKKU
KUK
C


a]5 ways.



10]Last week I painted a one-foot cube block of wood using red paint. Yesterday, I decided to cut this cube into smaller blocks, each 3 inches wide. How many of these smaller cubes had red paint on:

a) 4 of the sides?
b) 3 of the sides?
c) 2 of the sides?
d) 1 of the sides?
e) 0 of the sides?


a]From a total of 64 blocks:
a) 0.
b) 8.
c) 24.
d) 24.
e) 8.