Can you find the smallest non fractional number such that
If the number gets divided by 3 , we get the remainder of 1;
If the number gets divided by 4 , we get the remainder of 2
If the number gets divided by 5 , we get the remainder of 3;
If the number gets divided by 6 , we get the remainder of 4.
Two mathematicians Steven and James were sitting face to face when Steven came up with an idea in mind. He scribbled something on the table and told James to read it. James said that it was wrong. Steven said it is absolutely right.
What would Steven have scribbled to make both of them correct?
They have property such that when you light the fire from one end , it will take exactly 60 seconds to get completely burn.
However they do not burn at consistent speed (i.e it might be possible that 40 percent burn in 55 seconds and next 60 percent can burn in 10 seconds).
You can place weights on both side of weighing balance and you need to measure all weights between 1 and 1000. For example if you have weights 1 and 3,now you can measure 1,3 and 4 like earlier case, and also you can measure 2,by placing 3 on one side and 1 on the side which contain the substance to be weighed. So question again is how many minimum weights and of what denominations you need to measure all weights from 1kg to 1000kg.
There is no reason whatever why the customer's original deposit of Rs.100 should equal the total of the balances left after each withdrawal.
The total of withdrawals in the left-hand colum may equal Rs.100, but is is purely coincidence that the total of the right-hand column is close to Rs.100.
Let us show another example, but starting with Rs.200 in the bank:
Withdrawals Balance left
Moral of this story? Don't Total Balances
You have been given three jars of 3 liters, 5 liters and 8 liters capacity out of which the 8 liters jar is filled completely with water. Now you have to use these three jars to divide the water into two parts of 4 liters each.
How can you do it making the least amount of transfers?