Make The Sum With Four Sums Provided

In Make The Sum puzzles you find the numbers which make the sums you already see. Since there are multiple ways to create a single sum, all Make The Sum puzzles have multiple possible right answers. In this, the first of the Make The Sum series, the four initial horizontal and vertical sums are provided, and the student is required to provide one set of the several possible solutions for addends and the final, grand total.

The top row requires two numbers which sum to 5. In the next row you find two numbers which sum to 7. The two numbers in the left column must sum to 4 and the next column must sum to 8. The lower right corner, the grand total, will, of course, be 12. As you can see, there is more than one way to correctly place four numbers in the upper left four boxes. The true power and importance of Make The Sum lies in this fact, the multiplicity of solutions.

Let’s look at one approach to this puzzle. Since you must choose the numbers which add both across and down to the sums you see, start by picking one of them. In this case I will start by placing the number 3 in the top left.

Then choose that number which added to 3 will give 5. The answer, of course, is 2.

Now determine what value must be added to three to obtain four, which is one.

For the middle box you may either think of it as finding the number which added to two makes eight or the number which when added to one makes seven.

Finally you determine the grand sum in the lower right. You may either add down or right to obtain the sum 12.

Of course the student may choose a different digit to start, perhaps a four, two, one or even a zero.

There is no requirement that the student start in the upper left hand corner. Students may start by filling in any of the boxes. All of the puzzles in Make The Sum with four sums provided can be done using four distinct (different) digits from one to nine for the four upper left hand boxes, however that does not mean you should not allow other solutions.

You may allow the student to use zero, use doubles or triples, or come up with any type of solution. In fact, if a student is particularly creative or advanced, they need not restrict themselves to digits at all. They may choose to use negative numbers or fractions.

When students choose to go beyond the ten digits, the number of possible correct solutions becomes infinite.

See How Students Learn This Process in Critter Computation

Play Critter Computation