快猫短视频

#175 Wizard of odds

The students at Yellow Brick High School for Girls couldn鈥檛 decide if their maths and drama teacher, Ms Gale, was a genius or just overworked when she announced the new school play, a 鈥渕athemusical鈥� called The Wizard of Odds. But the real challenge, as usual, was in the casting, and the parents, students and faculty had various demands, summed up as follows:

1. If Megan doesn鈥檛 get the lead role, Dorothree, then Kasey will play either the Square Crow or the Ten Man.

2. If neither Leah nor Nicki are the Cowardly Line, Jane will be Dorothree.

3. If Leah doesn鈥檛 get the Square Crow, Jane or Kasey will get Dorothree.

4. If Nicki isn鈥檛 the Ten Man and if Leah doesn鈥檛 get Dorothree, then Kasey will play the Wicked Witch of the Word Problems.

5. If Leah isn鈥檛 the Cowardly Line and if Nicki isn鈥檛 the Wicked Witch of the Word Problems, then Jane will be cast as the Square Crow.

Remembering that 鈥渋f x, then y鈥� doesn鈥檛 imply 鈥渋f not x, then not y鈥�, can you help Ms Gale accommodate this tornado of requests by assigning the roles?

Solution next week

#174 Pieces of eight

Solution

The time spent in bed is 8 hours and 57 minutes.

Each of the four numbers on the digital alarm clock is made up using a conventional seven-segment display.

The 鈥�0鈥� uses six segments, the 鈥�1鈥� uses two, and so on, so the digits, from dimmest to brightest are: 1, 7, 4, (2, 3, 5), 0, (6, 9), 8, with numbers of equal brightness grouped in brackets.

The four clock digits can be 0-1, 0-9, 0-5 and 0-9. So the dimmest display possible is 11:11 and the brightest is 08:08.