A Math Game: Fun and Simple

I don’t know who invented this game so if you know it please comment below and let me know so I can cite the source. I think I first saw it on a Spanish TV show from the network TVE.

The players are given a sequence of numbers and a target, for example:

1, 1, 2, 13, 25 → 20

(the target here is 20)

The goal is to produce the target number using only the sequence of numbers and basic mathematical operations (addition, subtraction, multiplication and division). Brackets (parentheses) can be used as much as needed. For example 1×((13+25)÷2)+1 is a solution to the puzzle above. Another solution is (25+13+1+1)÷2. Notice that it is required that each number is used exactly as many times as it appears in the sequence.

This is one of the few puzzles which you can create yourself in a second and still be almost sure it has a solution as long as you add a couple of small numbers to the sequence. And even when it doesn’t have a solution, it is a nice challenge to get as close to the target as possible. On the Spanish tv show the winner was whoever found the exact number first or the one with the best approximation when the time was over.

Below are some puzzles, all of which have at least one solution. Write your comments and solutions in the comment section and let us know if you have more puzzles :). Have fun!

1, 3, 12, 13, 23, 54 → 99

2, 4, 5, 10, 81 → 18

3, 9, 23, 23, 45 → 17

16, 25, 43, 80, 90 → 1

20, 41, 62, 83, 100 → 66

4, 6, 21, 32, 44, 60 → 12

The Ken Ken Puzzle Craze

As you have probably guessed, KenKen puzzles have nothing to do with Barbie or Street Fighter. They are a relatively new kind of mathematical puzzle similar to Sudoku, developed last year by a rather unorthodox Japanese Math teacher named Tetsuya Miyamoto.

An unsolved KenKen puzzle looks something like this:

A 6x6 KenKen Puzzle

Since this is a 6×6 puzzle (there are also 4×4 and 8×8 KenKens), every row and every column must contain the digits from 1 to 6 in some order. Notice that each one of the heavily outlined cages has a target (a number) and an operation assigned to it. These parameters can be seen at the top-left corner of each cage. The numbers occupying the cells of a cage must produce its target after being combined in some order using its operation. A cage consisting of only one square doesn’t have an operation and must simply be filled up with its target. Here is an example of a finished 4×4 KenKen puzzle:

A Finished 4x4 KenKen Puzzle

Check out KenKen.com for more information and puzzles.