by Bill Graham

I took the time to figure out (from the clues above) how many coins in each bag so I could answer the question. Then with help from an Internet friend of mine, I found a much simpler approach. He wrote, "I started this with three equations. Then I had a 'Wait a minute!' experience. If each bag had a different number of coins and one set of four bags added up to 100, the only possible set to give this sum is 10+20+30+40, so Eli should take the other three bags which must contain 50, 60 and 70 coins." The 100 coins are in ACDE. So the ones the Eli should take are BFG.

Notice that Eli got 50+60+70=180 coins, not very fair for Robin, who did all of the work. The total number of coins is 280 = 10×(7×8÷2) from the equation for the sum of the first n numbers.