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

  1. Four 4's
  2. Five 5's
  3. Three Digits, Target 1-10
  4. Three Digits, Target 10-20
  5. Four Digits, Target 1-10
  6. Four Digits, Target 10-20
  7. Four Digits, Target 20-30
  8. Five Digits, Target 1-10
  9. Five Digits, Target 10-20
  10. Five Digits, Target 20-30
  11. Six Digits, Target 1-10
  12. Six Digits, Target 10-20
  13. Six Digits, Target 20-30
  14. Six Digits, Target 30-40
  15. Seven Digits, Target 1-30
  16. Seven Digits, Target 30-60
  17. Seven Digits, Target 60-100
  18. Eight Digits, Target 1-30
  19. Eight Digits, Target 30-60
  20. Eight Digits, Target 60-100
  21. Four Digits, Target 1
  22. Five Digits, Target 1
  23. Six Digits, Target 1
  24. Seven Digits, Target 1
  25. Eight Digits, Target 1
  26. Four Digits, Target 2
  27. Four Digits, Target 112
  28. Four Digits, Target 122
  
  1. Five Digits, Target 23
  2. Six Digits, Target 23
  3. Seven Digits, Target 23
  4. Eight Digits, Target 23
  5. Five Digits, Target 32
  6. Six Digits, Target 32
  7. Seven Digits, Target 32
  8. Eight Digits, Target 32
  9. Six Digits, Target 45
  10. Five Digits, Target 100
  11. Five Digits, Target 112
  12. Five Digits, Target 122
  13. Six Digits, Target 100
  14. Six Digits, Target 122
  15. Seven Digits, Target 100
  16. Eight Digits, Target 100
  17. Eight Digits, Target 122
  18. Nine Digits to 100
  19. 1 2 3 4 5 6 to 1-10
  20. 1 2 3 4 5 6 to 11-20
  21. 1 2 3 4 5 6 to 21-30
  22. 1 2 3 4 5 6 to 31-40
  23. 1 2 3 4 5 6 to 41-50
  24. 1 2 3 4 5 6 to 51-60
  25. 1 2 3 4 5 6 to 61-70
  26. 1 2 3 4 5 6 to 71-80
  27. 1 2 3 4 5 6 to 81-90
  28. 1 2 3 4 5 6 to 91-100

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Copyright © 1996-2017 Alexander Bogomolny

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