There are five thieves, each loot a bakery one after the other such that the first one takes 1/2 of the total no. of the breads plus 1/2 of a bread. Similarly 2nd, 3rd,4th and 5fth also did the same. After the fifth one no. of breads remained are 3. Initially how many breads were there?

• Answer Total breads were ---127
  
  Let the Number of Breads Initial be x
  
  You Should Go in Reverse Order as left Bread is 3
  i.e x=?
  
  After 1st person ate A=x-(x/2)-(1/2)
  i.e A=(2x-x)/2-(1/2)
  i.e A=(x/2)-(1/2)
  i.e A=(2x-2)/4
  i.e A=(x-1)/2
  
  like wise ----After 2nd person ate B=(A-1)/2
  
  like wise ----After 3rd person ate C=(B-1)/2
  
  like wise ----After 4th person ate D=(C-1)/2
  
  like wise ----After 5th person ate E=(D-1)/2
  
  Now as after 5th person ate the Value of remaining Bread is ---3
  
  therefore the value of E=3;
  
  Now go Reverse from botom to top to get the value of X after calcuating
  
  Value of D=7
  
  Value of C=15
  
  Value of B=31
  
  Value of A=63
  
  Value of X=127
  
  SO the Final answer is 127 breads were ther
• 9 years agoHelpfull: Yes(21) No(1)
• The best way of solving these kind of questions is reverse engineering, that is start from the end (memento movie approach)
  Before starting, lets understand the given condition in a much more comfortable way.
  The person will take half of the total bread ½ of one more slice of bread (greedy thief)
  So, let the bread present be x and the bread taken by the thief be y and the bread remaining be z.
  The reason for focus on bread remaining is it is the value given in the question and will be useful for our reverse engineering.
  From the x amount of bread available, the thief has taken (x/2) + (½)
  The bread left is almost half of the bread but (1/2) slice of bread less
  The amount of bread left is (x/2) – (½)
  So, the z defined by us ends up as (x/2) - (½)
  But z is the value given in the problem and we have to find out x
  So, lets tweak the relation
  z =(x/2) – (½)( by taking – (½) to the other side)
  z + (½) =(x/2) ( by multiplying both sides by 2)
  2z + 1 = x
  Now the process of reverse engineering,
  The bread left after 5th thief is 3 slices, that is z = 3, so the amount of bread when he entered , that is x = 2z + 1= 7
  Note that there are 7 slices before 5th thief entered implies that is the bread left after 4th thief
  The bread left after 4th thief is 7 slices, that is z = 7, so the amount of bread when he entered , that is x = 2z + 1= 15
  The bread left after 3rd thief is 15 slices, that is z = 15, so the amount of bread when he entered , that is x = 2z + 1= 31
  The bread left after 2nd thief is 31 slices, that is z = 31, so the amount of bread when he entered, that is x = 2z + 1= 63
  The bread left after 1st thief is 7 slices, that is z = 63, so the amount of bread when he entered, that is x = 2z + 1= 127
  So the total amount of bread initially is 127 slices.
  
  127 is the answer.
  
• 9 years agoHelpfull: Yes(13) No(0)
• solving from back side 3+1/2 present at last person before taken half and then double this amount present at the 5th person before distribution =7/2*2=7
  similarly at 4 th person=7+1/2 then 15/2*2=15
  similarly at 3 rd person=15+1/2 then 31/2*2=31
  similarly at 2nd person =31+1/2 then 63/2*2=63
  similarly at 1st person =63+1/2 then 127/2=127
• 9 years agoHelpfull: Yes(10) No(0)
• To Sandepunna
  
  If there are say seven slices of bread, the thief will take half of 7 slices that is three and half slices and one more half slice, so he will take a total of 4 slices and 3 slices will be left
  That is the reason the effect of eaach thief taking half more slice will be cancelled out
• 9 years agoHelpfull: Yes(1) No(0)
• its 65.....
• 9 years agoHelpfull: Yes(1) No(1)
• if five "1/2 " of a bread are taken out then how we would get an integer no i.e; 127 as initial no of breads ???
  just saying...
• 9 years agoHelpfull: Yes(0) No(0)
• total bread is 127
• 9 years agoHelpfull: Yes(0) No(0)
• .................................?crcr ans
• 9 years agoHelpfull: Yes(0) No(1)