A school has created a new software to make learning math easy and fun. The software has several games, to advance to next level the children have to solve some puzzles. In one such activity, there is a monkey and a mangoseller. The mangoseller asks the monkey to solve the following puzzle in return for a couple of mangoes. Counted in twos there were 1 mangoes that remained, counted in threes there were 2 that remained, counted in fours there were 1 that remained, counted in fives there were 2 that remained, counted in sixes there were 5 that remained and when counted in sevens there were none left. The activity then pops up a screen asking you if you can help the monkey guess the number of mangoes there were in the basket?

• Step 1: When counted in 2s, only 1 is left, that means the total no must be an odd no.
  Step 2: When counted in 5s, only 2 are left, that means the unit place of the total no must be (0+2=2) or (5+2=7). Again, the no must be an odd one. So the unit place of the total no must be 7.
  Step 3: When counted in 7s, none of the mangoes are left. That means the total no of mangoes must be a multiple of 7.
  Step 4: Now considering the count table of 7, the total no can not be any one of the nos upto 10 because total no can not be 7 as when 7 is divided by 6 only 1 is left and for the other nos on the count table of 7 upto 10 none would have 7 in their unit place. So, try for 77 and would satisfy all the conditions.
  Step 5: Total no of mangoes = 77.
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