Mathematical Fundamentals

In this sequence of problems, we want to know "is it possible?"

To solve each problem, try dragging the number tiles so that every row and column adds up to the target sum beside it:

Is it possible?

Is it Possible?

             

Now try this one.

Once you’ve solved this problem (if it's possible):
What is the smallest number in the top row of your solution?

Is it Possible?

             

This time the target sums are a sequence of values: 6, 7, 8, 9, and 10.

Once you’ve solved this problem (if it's possible):
What is the smallest number in the top row of your solution?

Is it Possible?

             

Solving puzzles that require you to think is a much better way to learn algebra than drilling rote procedures. You might speed up your arithmetic by drilling, but really understanding and strengthening your skills in algebra is about learning to see what numerical relationships and patterns are hidden within each problem.

Later in this course we'll more deeply explore the beautiful entanglement of algebra, number theory, and group theory at work in the mathematics of number grids. If you manipulate the numbers' positions systematically, you can make some powerful observations and connections:

Is it Possible?

             

Is it possible to solve this problem? If so, what number do you need to place in the center?

Is it Possible?

             

Now the target sums have changed...

Is it still possible to solve this problem? If so, what number do you need to place in the center?

Is it Possible?

             

This is the challenge in this sequence, and it's a tough one!

Strategy tip: If you add up the values on all of the tiles, you'd get that 1+2+3+4+5+6+7+8=36,1+2+3+4+5+6+7+8=36, and 36 is also the product of 12×3=12+12+12.12\times 3 = 12+12+12.

If it's possible, what four numbers wind up in the corners?

Is it Possible?

             
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