# Recycling numbers.

Here is a fun way to play with numbers. Think of any two-digit number like 23 or 87 or 33.

Let's begin with 42. ADD those two digits together: 4+2=6, and write down the 6.

Now we have 426. Add the last two digits together: 2+6=8. Write down the 8.

Now we have 4268. Add the last two digits again: 6+8=14, but write down ONLY THE LAST DIGIT (4).

Now we have 42684. Again adding the last two digits, we get 8+4=12, but write down ONLY THE 2.

Now we have 426842. BUT LOOK!!! It is starting to repeat. We are RECYCLING that number. The part that repeats (4268) is called a BRACELET. This bracelet has four links or

Let's try another number, say 50.5+0=5 Now we have 505. 0+5=5

So now it is 5055.5+5=10 Write down only the 0.

Now we have 50550. BEHOLD!! Again it is starting to repeat. This time the BRACELET (505) has three links.

What if we try 26? 2+6=8.

Therefore we have 268.6+8=14 Write down the 4.

We have 2684.8+4=12 Write down the 2.

We get 26842. Going on, we would get 268426842 and so on. But do you notice that this number (26) gives us the same repeating digits (and in the same order) as our first example (42) which gave us the BRACELET 4268. These BRACELETS (4268 and 2684) are considered to be "Lookalikes."

PROBLEM #1: What other two-digit numbers will give us Lookalikes to BRACELET 4268? __, __, __, or

PROBLEM #2: Are there any other two-digit numbers which will give us Lookalikes to BRACELET 505 (which we got from starting with 50)? __, or __,

PROBLEM #3: Let's start with the two-digit number 21. Do you get the following patterns: 213, 2134, 21347, 213471, 2134718, 21347189, 213471897, 2134718976, 21347189763, 213471897639, 2134718976392, 21347189763921, 213471897639213? STOP!! It is starting to recycle!! Therefore this BRACELET (213471897639) has 12 links. WHEW!! What other 2-digit numbers will give us the same 12-1ink BRACELET? __, __, __, __, __, __, __, __, __, __, __, or __,

PROBLEM #4: Find the BRACELET for the two-digit number 40.

1. (4268) will come from 26, 68, 84, or 42

2. (505 will come from 50 or 05 (This can be considered a 2-digit number.) or 55

3. (213471897638) will come from 21, 13, 34, 47, 47, 71, 18, 89, 97, 76, 63, 39, and 92

4. 40 gives us (40448202246062280886) This BRACELET has 20 links.

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