Inspired by this question, I rolled my own version (notice the solution is very different and not trivial):
Seven skillfull and smart D&D Lv. 20 thieves robbed a diamond shop at night. They ran to a nearby forest and then all slept there for the night. They didn't count how many diamonds there were in the bag, but anyway there can't be more than 400 diamonds in the bag since that's the bag maximum capacity.
- A thief wins the initiative roll, wakes up and runs away, but as soon as he tries to escape, a second thief catches him, and the second thief decides to divide the loot in 2. Unluckily, the remainder is 1 diamond.
- Meanwhile another thief wakes up and then tries to divide the loot, but as soon as he divides it the remainder is 2 diamonds.
- The 4th and 5th and 6th and 7th thieves wake up one by one. Each time the new thief tries to divide the loot equally, but they get 3, 4, 5, 6 diamonds as remainders, respectively.
- The last thief (7th and last to attempt loot division) then decides to give up the remainder to the other thieves before they even attempt to do some modulus calculations. Anyway only 1 thief is richer than him now.
Tell how many diamonds were in the bag and what happened.
Notice the emphasis and try to be on my side, I couldn't find a perfect fit, so I took the most immediate fit. Calculations are correct.
D&D stuff is just scenic.
Here's a list of what happens to make it even more clear (and thanks for comments!:) )
- Thief 1, try to escape
- Thief 2 stop the 1st and attempt division (remainder 1)
- Thief 3 stop the 1st,2nd and attempt division (remainder 2)
And so on..
- Thief 7 stop all previous thief and attempt division (remainder 6), then he distributes the remainder to the other thieves (1 diamond to thieves numbered from 1 to 6)
Before robbing the shop, the thieves have no money, and each diamond has equal value to other diamonds.
@GarethMcCaughan came up with the correct lateral thinking in his answer, however his solution (correct and acceptable, if no one find the elegant solution) is more complicated than needed (Indeed, I'm impressed by his skill, and I'm leaving open the chance to find the best answer!)
@Realdeo was succesfully in finding a exotic and fun explaination for the 7th thief returning part of the loot (though it is not the correct answer), I really enjoyed that answer from another D&D player.
There is a precise reason for wich the last thief give up the remainder. Indeed every thief don't know if others cheat and by wich quantity cheat. If you think in wich way I could create a puzzle like this you will find the simplest possible solution.