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#133 Think tank

Toddler Tina has noticed that Sticky, her stickleback, is struggling because the water in the slim fish tank is only 2 centimetres deep. She would like to top up the tank with water, but the tap is beyond her reach, so she has the bright idea of dropping one of her toy bricks into the tank instead.

Fortunately, the brick misses the fish, and the water level rises to become exactly level with the height of the brick, which is lying flat. The brick is twice as long as it is wide, and three times as long as it is high. The interior of the tank is one-and-a-half times as long as the brick, but only two-thirds as wide as the length of the brick.

What are the dimensions of Tina鈥檚 toy brick?

Solution next week

#132 One of these days

Solution

The quiz will be on Thursday. If it were on Monday, statement A would be false, B would be true and D would be true, making C false. Now, E can鈥檛 be true, because then it would become false, and it can鈥檛 be false, because then it would become true.

So there is a contradiction, telling us it can鈥檛 be on Monday. Similar logical contradictions exist for the other days except Thursday.