快猫短视频

#30 Digital targets

set by Peter Rowlett

You are playing a game in which you have to arrange 10 random single-digit numbers (which can include 0) to form five two-digit numbers, aiming for five targets: 10, 20, 30, 40 and 50.

If you match a target exactly, you score that number. If you get within 5 of a target, you score half the value of the target. Otherwise you score zero for that target.

For example, if you are given the numbers 1, 2, 2, 3, 3, 5, 5, 7, 8 and 9, you can arrange them to get a total score of 60, as shown in the table above (although this isn鈥檛 the optimal score with these numbers).

Which 10 single-digit numbers would let you make the maximum possible score?

What鈥檚 the highest score you can make if you are given the numbers 0, 1, 1, 2, 3, 4, 5, 9, 9 and 9?

If you were given one of each digit 0-9, what is the highest score you could get?

Solution next week

#29 Four by four

Solution

With an 8-centimetre length cut, the following divides the grid into two identical halves.

For a 10-cm cut, there are two ways of doing this.