Alphabet/number link

The following is an addition sum where each alphabet represents a distinct digit from among the 10 digits from 0 to 9-
    S  E  N  D
    M O  R  E
 -----------
M O N  E  Y
Find the actual addition sum as per those digits.

Filling up a sequence-two numbers to be filled up

Anybody willing to work out the next 2 numbers in the sequence below?-
7,7,2,4,3,3,4,3,7,2,3,?,?-
The answer is in the question itself.

Conversation with priest-Rejoinder

The organist could find the alternatives available for the values of ages where the product works out as 2450.As the sum of the ages was to be twice his own age and as he was unable to give the answer in the first instance,we can conclude his age as 32 and there were  2 alternatives available as (49,10,5) and (50,7,7) After the priest mentioned that he was the oldest,the organist could give answer.The logic works out as follows-If 'p' is the age of the priest and if p>50,he could not give the answer.If p<50,he could not be the oldest.So the organist concludes that p=50 and accordingly the ages of the visitors were 49, 10 and 5. 

One set of faulty coins

There are 10 sets of coins.You know how much the coins should weigh.You also know that all the coins in one set of 10 are exactly a hundredth of an ounce off,making that entire set of 10 coins a tenth of an ounce off.You are also told that all the other coins weigh the correct amount.You are allowed to use an extremely accurate digital weighing machine only once.How do you determine which set of 10 coins is faulty?

How to assign tasks

There was an organisation which had at a time the work of assigning 6 tasks to 6 persons on their roll.Each had to be assigned one task.Task 1 cannot be assigned to either person 1 or 2.Task 2 must be assigned to either person 3 or 4.In how many ways can the 6 tasks be assigned to those 6 persons?

Conversation between a priest and an organist in a church

The priest told the organist'Today there were 3 persons in the church besides us.The product of their ages was 2450 and the sum equal to twice your age.How old were they?' The organist who was clever,thought for a while and said'No,I cant figure that out'.The priest replied'If I tell you that I was the oldest person in the church today,can you solve the problem?'.The organist was able to do that.
Now comes a question for you-How old was the priest?  

Solutions for x^3+y^3+z^3=2

If we have the equation x^3+y^3+z^3=2,will it be possible to have integer solutions?
A first look will make you think that there  are none,but there are infinite number of solutions
You put x=1+p and y=1-p.You can then work out z as well as the value of p.
x^3+y^3=(1+3p+3p^2+p^3)+(1-3p+3p^2-p^3)=2+6p^2.
So we must have z^3=(-)6 p^2.
If p=(-)6a^3 ,we can get z^3=(-)6*(36a^6)=(-)216 a^6 and so z=(-)6 a^2
Thus the solutions are x=1-6a^3,y=1+6a^3 and z=(-)6 a^2 for any value 'a' can take
Example if a=2,we have x=1-48=(-)47,y=1+48=49 and z=(-)24
x^3+y^3+z^3=(49^3)-(47^3)-(24^3)=117649-103823-13824=2.