**This is a simple number guessing game. **

Ask your friend to think of a number (1-15) - don't tell

Show them 4 lists of numbers asking them to say yes or no if the number is on the list.

Tell them the number they were thinking of.

Easy.

### Supplies:

- Pencil
- Paper
- Scissors
- A friend

### Teacher Notes

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## Step 1: The Lists of Numbers and Guesing

**Building the game:**

- Cut a piece of paper into 4 strips. (Leave enough room to write 8 numbers).
- Write the following lists, one on each strip of paper

List A: | 1, 3, 5, 7, 9, 11, 13, 15 |

List B: | 2, 3, 6, 7, 10, 11, 14, 15 |

List C: | 4, 5, 6, 7,12, 13, 14, 15 |

List D: | 8, 9, 10, 11, 12, 13, 14, 15 |

**Playing the game:**

- Tell your fried to guess a number: (1-15) (don't tell).
- Show them each strip one and a time and ask if the number is on that strip.
- Every time they say "Yes" add the first number in the list to a total.
- After all lists have been reviewed, tell them the total of the first numbers of all the lists their number appeared in.

Example Game:

My number is 12.

I say "**No**" to List A

I say "**No**" to List B

I say **"Yes"** to List C (4 is first number)

I say **"Yes**" to List D (8 is first number)

4+8 =12 so my friend tells me 12 is my number.

## Step 2: Why This Works

**Although its not requires to understand this to use the lists:**

**Its simply Binary or Base2. ** As you may be aware binary is a list of 1s and 0s.

If we look at our numbers 1-15 and the binary number for the same value.

Decimal : Binary lists DCBA 1 = 0001 2 = 0010 3 = 0011 4 = 0100 5 = 0101 6 = 0110 7 = 0111 8 = 1000 9 = 1001 10 = 1010 11 = 1011 12 = 1100 13 = 1101 14 = 1110 15 = 1111

In binary or base 2 the rightmost number is 1, the next is 2 then 4 followed by 8. Think of the strips of paper as columns to hold numbers down the list. Every row with a 1 in the column would go on that strip. The first list "List A" would hold 1,3,5,7,9,11,13,15 because the right most number is a one. The number 7(111) would be in List A, List B and List C because there are 1's in the first, second and third places. In binary 111 would be in decimal 4+2+1 = 7.

**Challenge yourself:**

Want to take the numbers higher than 15? Binary number make a pattern, if we added a List E we could go to 31. The first number in List E would be 16. If we added a List F we could go to 63 and the first number in that list would be 32.

Here is a list for 1-31. Try it!!

List A List B List C List D List E 1 2 4 8 16 3 3 5 9 17 5 6 6 10 18 7 7 7 11 19 9 10 12 12 20 11 11 13 13 21 13 14 14 14 22 15 15 15 15 23 17 18 20 24 24 19 19 21 25 25 21 22 22 26 26 23 23 23 27 27 25 26 28 28 28 27 27 29 29 29 29 30 30 30 30 31 31 31 31 31

**There are 10 types of people, those who understand binary and those that do not!**

### If you like this Instructable please Vote for it!!

This is an entry in the

Made with Math Contest

## 8 Discussions

21 days ago

Fun way of learning math very nice 👍🏻

Reply 15 days ago

I like your projects as well.

5 weeks ago

I have never seen binary used like this, you are brilliant!!!

5 weeks ago on Step 2

Thanks for posting 1-31

6 weeks ago on Step 2

Good idea I really like it good job!

Reply 6 weeks ago

Thanks much, please vote if you liked it.

6 weeks ago on Step 2

I picked 7 and it doesn't work. Just put 7 in list C. Good game though!

Reply 6 weeks ago

7 is in list a,b and c. My first version I typo'ed it. If you don't see it there try refreshing your brower. Thanks,