# Make An Identity

Each page in the **Make An Identity** puzzle series offers several arithmetic problems of the same variety with slight modifications: given a sequence of digits and a target number, the task is to place the symbols of arithmetic operations (and sometimes a pair of parentheses) in-between the digits so as to get an arithmetic expression equal to the target number. The problems are simple math games as the games go but offer a splendid arithmetic practice suitable for various grades depending on the difficulty. The problems are presented with a Java applet.

As an example, the sequence of digits

1 1 1 6 8 with the target number of 10

can be resolved as

1 + 1 + 16 - 8 = 10.

The target number is placed in the brackets and always precedes the sequence of the digits. For example, the problem

[10]: 8 5 6 1 4

can be resolved as

8*5 - 6*(1 + 4) = 10.

The problems differ in the number of digits, the target, the allowed operations and the availability of parentheses. The solution is seldom unique; however, all problems have a solution in integer arithmetic. You can get one such solution be pressing the **Help** button whenever it is available at the bottom of the applet.

Originally, each problem, i.e. a row of digits, contains clickable areas in front and rear and in-between the digits. If so desired, these can be removed by clicking the **Shrink** button, or expanded by clicking the **Expand** button. To get accustomed to the applet device, play withe the two buttons. Most often the number of spaces - past and present, i.e. the number of clickable areas, is excessive. A problem will look much nicer if you press **Shrink** followed by **Expand**. Use **Expand** also wherever there is no room for additional insertion. But **Expand** will add too many spaces, so, after the desired insertion press **Shrink** and **Expand** in succession.

Clicking on such areas brings up a selector list to pick up an allowed symbol. These is done by a double-click. If you wish to observe the clickable areas, check the box **Where to click**. The built-in expression evaluator ignores the spaces. In particular this means that multidigit numbers can be used freely.

### Make An Identity

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