# The Diana On the target that is drawn next to these lines there are sectors marked with scores 13, 15, 19 and 10.

Where do you have to give the least number of shots to add 100?

#### Solution

If we divide 100 by the largest of the numbers, 19, we get more than 5 shots (6 * 19 = 114). That means that we will need at least 6 shots to get 100, because with 5 we can only reach 95 (5 * 19). Let's try the combinations of 6 bigger shots.

As we have already seen, 6 * 19 = 114 and we passed.

The following situation, 5 * 19 + 1 * 15 = 110, we also pass, as if we change the success in 15 by one of 13 (108), or one of 10 (105).

If we take 4 * 19 = 76 and add 2 * 15, we get 106. Nor do we get 100 if we change one from 15 to 13 (104) or 10 (101).

If we add to 4 * 19 = 76, two hits in 13, we get 102, if we change one for a 10, 99, and if we change both, we will still get less.

That is, that 4 shots in 19 leaves us no solution. Let's try 3 shots in 19, which gives 57.

If we add another 3 in 15 (45), it gives us 102, which doesn't work for us either. But when changing one of them for a 13, it does allow us to add 100 (19 + 19 + 19 + 15 + 15 + 13).