10 prisoners are locked up in individual cells, unable to see, speak or communicate in any way with each other. There is a exercise room with a single light, that is initially off and the prisoners cannot see the light from their own cell.
Every day, the warden picks a prisoner at random, and that prisoner goes to the exercise room.
While there, the prisoner can choose to switch the light on or off, and are not allowed to leave a message.
At any point, any prisoner can claim that all 10 prisoners have been to the exercise room. If they are wrong then all 10 prisoners will locked up forever! However, if they are correct all of the prisoners are set free.
Before the random picking begins, the prisoners are allowed to discuss a plan. What is their best plan to determine when all 10 prisoners have visited the exercise room?
[Ref: ZAWX]
Hint: Remember that once the picking starts, there is no method of communication.
Answer:
One person is chosen as a Counter and will only ever turn the light off, and they will count the number of times they do this.
Each of the other prisoners will only turn the light on once. They will only touch the light if it's already off - and only if they've not yet turned it on.
Ever time the Counter goes to the exercise room, if the light is on again, they'll know a new person has entered the room, and they'll turn the light off.
Once the Counter has turned the light off 9 times, they will know that the other 9 prisoners have entered the room, and therefore can ask for everyone to be released.
For 10 prisoners, on average, this would take around 91 days.
For 20 prisoners, on average, this would take around 381 days.
For 50 prisoners, on average, this would take over 6 years.
For 100 prisoners, on average, this would take over 27 years.
Puzzle 392
My 10, 8, 3 is a boisterous lad.
My 9, 4, 8, 7 is the underground part of a tree.
My 6, 5, 7 is admired by some.
My 3, 4, 1, 7 can be used to keep a door shut.
My 2, 1, 7, 6, 9 is where we pray.
My whole is where some discoveries are made.
If cat and a half can catch a mouse and a half in a day and a half how many mice can 3 cats catch in 3 days?
[Ref: ZSSR]
Hint: How many mice does one cat catch?
Answer: Six mice.
1.5 cats catch 1.5 mice in 1.5 days.
so
1 cat catches 1 mouse in 1.5 days.
1 cat catches 2 mice in 3 days.
Therefore
3 cats catch 6 mice in 3 days.
Puzzle 394
The four clowns in this puzzle all competed for the much-prized 'Clown of the Year' award recently. There were 30 clowns in total who entered the competition and each had to make the judges laugh.
From the clues below, can you work out each clown's name, the town he or she came from, what place each clown was awarded and the most comical moment of each clown's routine?
1. The Budsworth clown finished one place lower than Strumpy who is not from Witfield.
2. The judges roared with laughter as one clown cycled across a tightrope, wobbled, screamed and fell head first into a pool of water. He finished two places below Boo Boo who was not from Witfield.
3. The clown who finished in 7th place lost points when her big red nose fell off during her manic routine. This involved being hit with a giant rubber mallet by her assistant who was supposed to hit her on the shoulder but unfortunately had something in his eye at the time and accidentally bashed her in the face instead.
4. Tambo was disappointed when his usually masterful custard pie antics failed to impress the judges sufficiently to secure the award. He was not the clown from Stockville whose final placing was lower than the Shrimpton clown.
Name Town # Routine
Boo Boo Shrimpton 2nd Flower
Strumpy Stockville 4th Unicycle
Tambo Budsworth 5th Custard Pie
Grego Whitfield 7th Rubber Mallet
The positions that the four clowns could finish are 2nd, 4th, 5th and 7th. The Budsworth clown finished one place below Strumpy (1) so Strumpy must have been 4th and the Budsworth clown 5th. The (male) clown on the unicycle finished two places below Boo Boo (2) so must have been 7th or 4th. Since the clown who came 7th was female, the clown on the unicycle must have been 4th and is Strumpy and Boo Boo came 2nd. Tambo (male) is not the clown who came 7th (3), 2nd (Boo Boo) or 4th (Strumpy) so came 5th with his custard pie act (4) and Grego came 7th with her rubber mallet so by elimination, Boo Boo's act involved the flower. The Budsworth clown (Tambo) came 5th, neither Strumpy (1) nor Boo Boo (2) came from Whitfield so the clown from Whitfield was Grego (7th). The Shrimpton clown was placed higher than the Stockville clown (4) so came 2nd and the Stockville clown came 4th.
Puzzle 395
Using the BrainTracker grid below, how many words can you find? Each word must contain the central M and no letter can be used twice, however, the letters do not have to be connected. Proper nouns are not allowed, however, plurals are. There is at least one nine letter word. Excellent: 21 words. Good: 16 words. Average: 12 words.
Puzzle 391
