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.