Page 287 - ABCTE Study Guide_Neat

Identify the following four-digit number when presented with the following information:

1. One of the four digits is a 1.

2. The digit in the hundreds place is three times the digit in the thousands
place.

3. The digit in the ones place is four times the digit in the ten's place.
4. The sum of all four digits is 13.
5. The digit 2 is in the thousands place.

Help your students identify and prioritize the information presented.

In this particular example, we want to look for concrete information. Clue #1 tells us that one digit is a 1,
but we’re not sure of its location, so we see if we can find a clue with more concrete information.

We can see that clue #5 gives us that kind of information and is the only clue that does, so we start from
there.

Because this clue tells us that the thousands place digit is 2, we search for clues relevant to this clue.
Clue #2 tells us that the digit in the hundreds place is three times that of the thousands place digit, so it is
6.

2 6 _ _

So now we need to find the tens and ones place digits, and see that clue #3 tells us that the digit in the
ones place is four times the digit in the tens place. But we remember that clue #1 tells us that there's a
one somewhere, and since one is not four times any digit, we see that the one must be in the tens place,
which leads us to the conclusion that the digit in the ones place is four. So then we conclude that our
number is:

2 6 1 4

If you were following closely, you would notice that clue #4 was never used. It is a nice way to check our
answer, since the digits of 2614 do indeed add up to be thirteen, but we did not need this clue to solve the
problem.

Recall that the clues' relevance were identified and prioritized as follows:

1) clue #5

2) clue #2

3) clue #3 and clue #1

By identifying and prioritizing information, we were able to make the information given in the problem
seem less overwhelming. We ordered the clues by relevance, with the most relevant clue providing us
with a starting point to solve the problem. This method also utilized the more general method of breaking
a problem into smaller and simpler parts to make it easier to solve.

Now let's look at another mathematical problem and another general problem-solving method to help us
solve it: