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)**.