This week's maths problem

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Problem of the week

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On Friday of each week we will post a new maths challenge.
You may submit your solution by the following Thursday.
Each problem contains two different levels of difficulty. You will be awarded from 2 to 12 points for a full answer.
Each series contains 12 problems before the stage winner is determined.
Your score will be published here.

In each series we will give away 3 books as prices. The prices will be drawn by lot among the best ten participants of the series. The books are kindly sponsored by Buchdienst Rattei of Chemnitz.

Suggestions for problems are welcome.

Deadline is 8th. August 2024.

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Series 67

problem 793

logical task

Lisa and Mike want to go to the concert and have already made a note of the following: Udo Lindenberg, Mungo Jerry, Ozzy Osborne, Rolling Stones and Sting will be playing. The concerts will take place on 6, 13, 14, 21 and 28 October. The concert tickets (per person) are quite expensive, so there can only be a maximum of two concerts. (Prices: € 224, € 230, € 232, € 233 and € 240) The concerts themselves start at 8.00 pm, 8.30 pm, 8.45 pm, 9.00 pm and one even at 9.30 pm.
Lisa has noted down some more information.
1st the concert on 21.10. starts at 20.00.
2nd the concert on 6 October does not start at 8.45 pm. The tickets for the concert on 6 October and for the concert that starts at 8.45 pm are cheaper than the tickets for Mungo Jerry. The Rolling Stones are not performing on 6th October, nor do they start at 8.45 pm.
3rd the tickets for the concert that starts at 8.30 pm are more expensive than for the Ozzy Osborne concert.
4th Udo Lindenberg starts at 9.00 pm.
5th the tickets for the concert that starts at 9.30 pm are the most expensive. The cheapest tickets are for 14th October.
6th the Mungo Jerry concert starts half an hour earlier than the Rolling Stones concert.
7th tickets for the Rolling Stones concert cost 230 euros each. It does not take place on 28th October.
When does which concert take place? When do the concerts start and what are the ticket prices? 6 blue points

While Lisa and Mike are still going about their appointments, it starts to rain heavily outside. Looking out of the window, they see that 30 people have taken shelter under a canopy by the bus platform. ‘I hope the buses are on time,’ says Lisa. Bus routes 7, 14, 42, 84 and 126 depart every 4, 7, 9, 11 and 12 minutes respectively, with destinations in Drei-Stein, Eins-Heim, Hundert-Wasser, Neun-Dorf and Vier-Singen. As Lisa discovered afterwards, 4, 5, 6, 7 and 8 passengers boarded the buses. A quick look at Mike's note.
1st four people got on after Vier-Singen, but that wasn't the number 14 bus.
2nd the number of passengers who had to wait nine minutes for the number 42 bus after the rain started was greater than the number of people who wanted to go to Neun-Dorf.
3rd when the rain started, the display board said that the bus to Eins-Heim would leave first.
4th Bus number 7 goes to Drei-Stein.
5th 6 people got on the last bus.
6th exactly one more person boarded the bus travelling to Hundert-Wasser than the bus on route 84, meaning that fewer people travelled to Hundert-Wasser than on the bus for which there was a 7-minute wait.
After the last bus had left, the rain stopped and Lisa and Mike got home dry on their bikes.
How many people got on each bus line? Where did the buses go and how long did people stand under the canopy? 6 red points

Deadline for solution is the 8th. August 2024.
 

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