While house hunting in London, I came across a very good leasehold property Discussing the lease the landlady told me:
'The property was originally on a 99 years lease and two-thirds of the time passed is equal to four-fifths of the tme to come. Now work it out for yourself and see how many years are to go!
can you find four numbers such that the sum of every two and the sum of all four may be perfect squares?
Besides several other answers, the smallest numbers that satisfies the conditions are:
a = 10430, b = 3970, c = 2114, d = 386
a + b = 10430 +3970 = 14400 =`120^2`
a + c = 10430 + 2114 =12544 = `112^2`
a + d =10430 + 386 = 10816 = `104^2`
b + c = 3970 + 2114 = 6084 = `78^2`
b +d = 3970 + 386 = 4356 = `66^2`
c + d = 2114 + 386 = 2500 = `50^2`
a + b + c + d = 10430 + 3970 + 2114 + 386
= 16900 = `130^2`
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?
One train was running just twice as fast as the other
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. Ony 6 cuts of saw or necessary to do this, while keeping the pieces together. now, can you reduce the number of cuts by rerranging the pieces after each cut? If you can. how is it done? if you can't, why can't it be done?
It cannot be done in less than six cuts. because the cube which is formed in the middle of the original cube has no exposed surface.
Since a cube has 6 sides, the saw must create this cube by 6 passes of the saw, no matter how the slices are rearranged.
I have a money pouch containing Rs. 700. There are equal number of 25 paise coins, 50 paise coins and one rupee coins.
How many of each are there?
25 paise + 50 paise + 100 paise = 175 paise and Rs. 700 = 70,000 paise
`(70,000)/(175)` = 400
400 is the number for each denomination