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There is a vessel of capcity 10 litres filled with milk and two empty vessels of capacities 3 litres and 7 litres. What is the minimum number of steps required such that 10 litre vessel and 7 litre vessel contain 5 litre each ?(1 step is defined as one transfer of milk from one vessel to another).

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  1. From the 10 litres fill the 3 litre "twice" each time, pour the 3 litres into the 7 litres container. (4 transfers)

    You now have 4 litres in the 10 litre can and 6 litres in the 7 litre can.

    Now fill the 3 litre can from the 10 litre can. (1 transfer)

    You now have 1 litre in the 10 litre can, 6 litres in the 7 litre can and 3 litres in the 3 litre can.

    Now top off the 7 litre can from the 3 litre can and 2 litres  remain in the 3 litre can. (1 transfer)

    You now have 1 litre 7litres  and 2 litres

    Pour the 7 litre into the 10 litre can and the 2 litre into the 7 litre  can. (2 transfers)

    you now have 8 litres, 2 litres and 0

    From the 8 litre fill the 3 litre - this leaves 5 litres in the 10 litre can. (1 transfer)  Pour the 3 litre into the 7 litre and you now have 5 litres in each. (1 transfer)

    Total = 10 transfers


  2. Dump 5 liters from the 10 liter container to the 7 liter container.

    So thats...1 step

  3. One simple step. pour 5 litres of milk from the 10 litre vessel into the 7 litre vessel.

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