1. ## 1-100 project

I'm not sure if any of you have done this project in the past, but it's called the 1-100 project. Your given 4 numbers, for example mine is 3 6 7 8. You have to use any of the following: addition, subtraction, multiplication, division, square root, powers, and factorials, to get all the numbers between 1 and 100 inclusive. You can also change the numbers into fractions/decimals and put two numbers together to make a larger number (like I can use 3 and 7 not just as 3 and 7 but also 37 or 73.) You also have to use all four numbers, each one only once. For example, for the number 12 I did 3+8+(7-6). I was wondering if anyone had some spare time to help me with some of the numbers since it's due next week and I don't know if I can do them all on my own. So here's the numbers I don't have yet:

9, 13-23, 25-34, 36, 38-49, 51-59, 61, 63, 65-68, 70-74, 77-79, 82, 83, 86-88, 91-95, 97-100.

Ya I know i don't have that many done... that's why i'm asking for help...

2. It is amazing to me that any child relates to mathematics after having been subjected to obvious make-work projects like this. However, you have to do it. The basic idea is not to try doing them in order but to find some techniques that can be applied over and over.

First, write down all the numbers from 1 to 100 on one piece of paper.

Now get a second piece of paper to do the real work on. What you need to do is to create an inventory of "tricks." For example, you can create 67 and 76 easily from the 6 and the 7. So let's start with 76. Now what can you with 3 and 8?

$76 + 3 + 8 = 87.$ Write this down beside 87 on the first piece of paper.

$76 - 3 + 8 = 81.$ Write this down beside 81.

$76 + 3 - 8 = 71.$ Write this down next to 71.

$76 - 3 - 8 = 65.$ Write this down next to 65.

$76 + 3 * 8 = 100.$ Write this down next to 100.

$76 - 3 * 8 = 52.$ Write this down next to 52.

This gave you 6 numbers scattered all around. So now you can work with 67 the same way. When you are done with 67, can you see how to vary this trick?

I'll let you continue what is a fairly mechanical exercise. What you will find is that you get more than one way to form certain numbers, which probably is the point of the exercise. Moreover this one "trick" I have showed you will not generate 100 numbers. (It will generate fewer than 72.) So you will have to find at least one more "trick" that can be varied systematically the way this one was.

You should be able to get close to 100 numbers by completing this trick and by finding one more that can be applied over and over. If you can't get all the way to 100 numbers, please come back with a list of the ones remaining and tell us your second trick. Then we can help you find a third trick.

3. Since the factorial is allowed:
(7 - 3)! = 4! = 24
Now combine 24 with 6 and 8; like:
24 + 68 = 92
24 + 6*8 = 72
...carry on
That's another "trick a-la-Jeff"!

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