While house hunting in London, I came across a very good base hold property. Discussing the lease the landlady told me: “The property was originally on a 99 years lease and two-thirds of the time past is equal to four-fifths of the time to come. Now work it out for yourself and see how many years are there to go”! How many years of unexpired lease did the property have?
The squares
Can you find four numbers such that the sum of every two and the sum of all four may be perfect squares?
The two trains
Two trains start at the same time, one from Bangalore to Mysore and the other from Mysore to Bangalore. If they arrive at their destinations one hour and four hours respectively after passing one another, how much faster is one train running than the other?
Sawing the cube
We have a wooden cube of 3" on a side and we have a buzz-saw. The cube can be cut into 27 one inch cubes by the buzz-saw. Only six cuts of saw are necessary to do this, while keeping the pieces together. Now, can you reduce the number of cuts by rearranging the pieces after each cut? If you can, how is it done? If you can't, why can't it be done?
A matter of dollars and cents
I have a money pouch containing $700. There are an equal number of 25 cents coins, fifty cents coins and one dollar coins. How many of each is there?
The house where she lives
It was at a cocktail party in New York that I met Stephanie. We exchanged our phone numbers and decided to meet each other soon. When she rang up and invited me to her house this is how she gave me the number of her house: “I live in a long street. Numbered on my side are the houses one, two, and three and so on. All the numbers on one side of me add up exactly the same as all the numbers on the other side of me. I know there are more than fifty houses on that side of the street, but not so many as five hundred”. Can you find Stephaine's house number?
The mango thieves
One night three naughty boys stole a basketful of mangoes from a garden, hid the loot and went to sleep. Before retiring they did some quick counting and found that the fruits were less than a hundred in number. During the night one thief awoke, counted the mangoes and found that he could divide the mangoes into three equal parts if he first took one for himself. He then took one mango, ate it up, and took 1/3 of the rest, hid them separately and went back to sleep. Shortly thereafter another thief awoke, counted the mangoes and he again found that if he took one for himself the loot could be divided into three equal parts. He ate up one mango, bagged 1/3 of the remainder, hid them separately and went back to sleep. The third thief also awoke after some time, did the same and went back to sleep. In the morning when they all woke up; and counted their mangoes, they found that the remaining mangoes again totaled one more than could be divided into three equal parts. How many mangoes did the boys steal?
The farmer and the animals
Farmer Thimmayya bought some mules at $50 each, sheep at $40 each, goats at $25 each, and pigs at $10 each. The average price of the animals per head worked to $30. How many animals of each kind did he buy?
The rose garden
In my bungalow in Bangalore I have a beautiful rose garden. The four sides of the garden are known to be twenty, sixteen, twelve and ten rods. And it is also known that it has the greatest possible area for those sides. Can you find the area?
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