#134 No time to try
James Blond edges along the corridors of the supervillain鈥檚 base, and comes to two locked doors, each with a keypad that requires a four-digit code. He will need to get through one of the doors, but there is no time to guess a four-digit code 鈥� the number of possible combinations is staggering!
But wait! Some of the buttons on the keypads are visibly worn down, while others look as if they have never been pressed.
One door has a keypad with four worn buttons, the other has three. Blond only has time to try one door, and he will have to try all the possible combinations.
Which of the two keypads will give him fewer combinations to try 鈥� the one with four worn buttons, or the one with three?
#133 Think tank
Solution
The brick dimensions are 12 by 6 by 4 centimetres. If we call the brick length L, then we can take the base area of the tank (3L/2) 脳 (2L/3) and subtract the area of the brick resting on the bottom of the tank L 脳 (L/2).
We then multiply the result by the new water height L/3, which is the height of the brick. The expression obtained should equal the volume of water (including the fish) in the tank, (3L/2)(2L/3) 脳 2, calculated without the brick. This gives the equation L3/6 = 2L2.
The only solutions are L = 0 (invalid) and L = 12 cm. The calculations L/2 and L/3 give the width and height of the brick, respectively.
Quick quiz #122
1 Epigeal, hypogeal and viviparous are three types of which process?
2 In what year was a magnetar observed for the first time?
3 The Devonian, the Carboniferous and the Silurian periods all occurred in which geological era?
4 Hydrogen cyanide was first derived from which synthetic pigment?
5 What is the highest active volcano in the world?
Answers
1 Germination
2 1979
3 The Palaeozoic era
4 Prussian blue
5 Ojos del Salado, on the Argentina-Chile border. It is 6893 metres high