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A thief steals half the total number of loaves of bread plus 1/2 loaf from a bakery. A second thief steals half the remaining number of loaves plus 1/2 loaf and so on. After the 5th thief has stolen there are no more loaves left in the bakery. What was the total number of loaves did the bakery have at the beginning ?

Correct Answer: 31

Let y be the total number of loavesa be the remaining loaves after 1st thiefb be the remaining loaves after 2nd thiefand c, d..so on after 3 and 4 the = 0 be the remaining loaves after 5th thief

a = y - (y/2 + 1/2)= y/2 - 1/2

b = a - (a/2 + 1/2)= a/2 - 1/2

c = b - (b/2 + 1/2)= b/2 - 1/2

d = c - (c/2 + 1/2)= c/2 - 1/2

e = d - (d/2 + 1/2)= d/2 - 1/2we know that, e = 0,thus by substitution, we getd = 1c = 3b = 7a = 15y = 31Therefore total number of bread loaves in bakery was 31.

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