Solution:

This particular answer depends on what the third person says.

You know that the other two logicians have 20 and 30 painted on their foreheads. If the first logician is 10, the second will either say he has either 40 or 20 painted on his forehead. The second logician will say "I'm either 30 or 10 but I can't be 10 because every number is unique as explained earlier. If the third logician is able to deduce that he has 30 painted on his forehead, but the third logician is not able to deduce the number. Thus the first logician is not numbered 10 and he must be painted 50 on his forehead.

Solution:

Side A = 3 Cannibals, 3 missionaries
Side B = 0 Cannibals, 0 missionaries

1 cannibal and 1 missionary goes in the boat
Side A = 2 Cannibals, 2 missionaries
Side B = 1 Cannibals, 1 missionaries

1 missionary returns back and 2 cannibals go there
Side A = 0 Cannibals, 3 missionaries
Side B = 3 Cannibals, 0 missionaries

1 cannibal returns and 2 missionaries go
Side A = 1 Cannibals, 1 missionaries
Side B = 2 Cannibals, 2 missionaries

1 missionary and 1 cannibal return and 2 missionaries go
Side A = 2 Cannibals, 0 missionaries
Side B = 1 Cannibals, 3 missionaries

One cannibal back, two cannibals go
Side A = 1 Cannibals, 0 missionaries
Side B = 2 Cannibals, 3 missionaries

One cannibal back, two cannibals go
Side A = 0 Cannibals, 0 missionaries
Side B = 3 Cannibals, 3 missionaries

Thus all have crossed successfully

Solution:

John starts after 3 days, thus Peter has already covered 60 km by then (travelling at 20km a day)
The distance between Peter and John will be increased to 60 + 5 + 1 = 66 km in the next two days.

Since John is following an arithmetic progression in the speed daily, the distance between him and peter will keep on decreasing from the 6th day. It will decrease by 3 km on the first day, 7 km on the next day and so on.

Now John will catch up with Peter after n + 5 days from the start of Peter
Thus
66 = (n/2)*(2*3 + (n-1)*4)

If we solve for n in the above equation, we will get n = 5.5

Thus John will catch up with Peter on the eights day when he starts running after Peter.

Solution:

You can do it by two methods. However, we are explaining only one and leaving one for you to figure out yourself.

What you will do is fill the 3 liters jar and pour it into the 5 liters jar. Fill the 3 liters jar again and pour it into the 5 liters jar till it's full. Now we know that the 5 liters jar was already having 3 liters of water, thus you would be able to fill 2 liters only. In that case, the 3 liters jar will be left with 1 liter water. Empty the 5 liters jar and then pour the remaining 1 liter from 3 liters jar to the 5 liters jar. Refill the 3 liters jar and pour it completely into the 5 liters jar which already had 1 liter water. Thus now the 5 liters jar have 4 liters of water.

Solution:

The argument of Chris Evans is quiet flawed as he fails to differentiate between purchasing and consuming.