Four friends meet every Monday to play marbles. At the end of the games played today, just before the monthly tally was going to be recorded, Andrew accidentally tripped over the table, knocking all 100 competition marbles to the floor. The last time they had recorded a count of everyone’s marbles was four weeks ago. They did, however, each record some of the information from their individual, weekly games.
End of the first competition of the month:
- Before losing a third of his marbles to Matt, Louis had 11 more marbles the previous week than what Andrew has today.
- Rob picked up 1 marble from his game with Matt, but beat Andrew by enough so that Rob's new total matched what Andrew had last week.
End of the second competition:
- Andrew lost a fifth of his marbles to Rob in his first game, then lost a fifth of his remaining marbles to Louis in his second game.
- Matt picked up 2 marbles from each of his games with Rob and Louis.
End of the third competition:
- In beating Louis, Matt now has twice as many marbles as Andrew had the previous week.
- Andrew's number of marbles, by taking 8 marbles from his game with Rob and also beating Louis, is equal to the average of Rob's and Louis's marbles from the previous week.
End of today's fourth competition:
- Matt lost to both Rob and Andrew, losing a total of 22 marbles.
- Rob beat Louis, who in turn beat Andrew, so that now Rob has 4 more marbles than Louis, who in turn has 4 more marbles than Andrew.
After the totals were read from a month ago, Matt said, "Hey, that's funny. I just remembered how many marbles I had at the end of today, and I've only lost one in the last month!"
Can you figure out how many marbles everyone should have at the end of today's competition? Can you figure out how many marbles everyone should have had at the end of every competition this month?