manager vs manger Riddles

For 4 numbers: 1 + 1 + 2 + 4= 1 x 1 x 2 x 4. For 5 numbers: 1 + 1 + 1 + 2 + 5= 1 x 1 x 1 x 2 x 4 1 + 1 + 1 + 3 + 3= 1 x 1 x 1 x 2 x 4 1 + 1 +2 + 2 + 2= 1 x 1 x 2 x 2 x 2

Yes, a 100 dollar bill will always be worth more than a one dollar one.

The maid. A Japanese flag is the same from all sides, with a red dot in the center of a white background.

Let's say 6 statements are lies. A's 1st statement and C's 1st statement negate each other. One of them is a lie. C's and D's negate each other. One of them is lying. Therefore, there are 4 additional false statements. Assume A is guilty. If so, A's second statement, B's second statement, and D's first statement are the additional lies. Assume D is guilty. If so, A's second statement, B's first statement, and D's third statement are lies. This also only makes five false statements. D did not do it. Assume C did it. If so, A's second statement, D's first and third statements are false. This again, makes only five false statements. After ruling out suspects A, C and D, B is the culprit. B's third statement, C's second statement, and D's first and third statements are the additional false statements. This adds up to six.