Problem number 20. Three squirrels, Annie, Asia, and Ellie, collected seven nuts in total. Each collected a different number of nuts, but each collected at least one nut. Annie collected the least and Asia the most. How many nuts did Ellie collect? A1, B2, C3, D4, E5. One way to solve this problem is to try different numbers starting with one nut for the number of nuts collected by the squirrel who collected the least and trying to get them to add up to seven. Here are three squirrels. Let's label them in order starting with the one that collected the least. Annie collected the least so this will be her here. Asia collected the most so this will be Asia and Ellie will be the one who is in the middle. Now let's try different numbers and figure out how to make it so that they collected seven nuts in total. If Annie collected one nut, it's possible that Ellie collected two nuts because two is more than one. If that's the case, that makes three nuts so Asia would have had to collect four nuts to make seven nuts total. So this would work. If Annie collected one nut and Ellie collected three nuts, that gives us four nuts and Asia would have to collect three nuts if there was a total of seven nuts. This does not work because Asia then did not collect more nuts than Ellie so this doesn't work. Also if Annie collected one nut and Ellie collected four nuts, that's five nuts and we would need to add two more to the total that was collected to make seven and again that is not more than Ellie collected so that doesn't work either. So if Annie collected one nut then Ellie must have collected two nuts and Asia four. Now let's try with Annie collecting two nuts. Then Ellie must have collected at least three nuts. Two plus three is five and then Asia would have collected two nuts which is less than what Ellie collected so that's not going to work. So we already know that it's not going to work if we say that Annie collected two nuts because there's no way to make Asia collect more nuts than Ellie then. If Annie collected three nuts, Ellie must have collected at least four nuts and that already gives us seven so that's not going to work. Now we see that the only set of numbers that works is Annie collecting one nut, Ellie collecting two nuts, and Asia collecting four nuts which means that Ellie collected two nuts. This is answer B.

squirrels

nuts

distribution

Annie

Ellie