a) Is it possible to distribute 20 coins with denominations of $1, 2, 3, \ldots, 19, 20$ mungu into three pockets so that the amount of money in each pocket is the same?

b) And if you add one more tugrik? (As is known, one tugrik equals one hundred mungu.)
a) For example, you can put coins worth 20, 19, 18, and 13 mungu in the first pocket, -17, 16, 15, 14, and 8 mungu in the second pocket, and 12, 11, 10, 9, 7, 6, 5, 4, 3, 2, and 1 mungu in the third pocket. Thus, each pocket will contain 70 mungu.

b) The total number of mungu is $210+100=310$ mungu, but 310 is not divisible by 3.

## Answer

a) Yes; b) No.