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Consecutive Numbers

Sent in by:
Elisa of Potomac, MD

Do you like math puzzles? Well, here's a great one!

## Materials Needed

• some mathematical logic

## Instructions

1. Find five consecutive numbers that add up to 100. Consecutive numbers are numbers that come in a row, like 4, 5 and 6 or 30, 31 and 32.
2. Once you know which five consecutive numbers equal 100, try to figure out which five consecutive numbers equal 200. After you do that, you'll probably see a pattern.
3. Use the pattern to see which five consecutive numbers add up to 300.

Did you find a pattern? For an added challenge, figure out what you would have to do to find six or seven consecutive numbers that add up to 100. Do you know any other challenging math puzzles? If so, challenge ZOOMers the world over by sending them to ZOOM!

Baily, age 9 of London wrote:
it was hard but I figgered it out. the nubers are18+19+20+21+22=100.

Youngky, age 14 of HI wrote:
It was hard but you add ten each time. It is 18+19+20+21+22=100

Sarah, age 13 of Victoria wrote:
I got the average of one hundred which was 20 and I said well 20 is the average so I must take 2 numbers bofore 20 and 2 numbers after it so there would be five numbers so the answer was 18, 19, 20, 21 and 22

Febby, age 12 of Dumaguete, Phil. wrote:
The trick is for every 100, the digits will increase by 20 to obtain the answer for 100, its 18,19,20,21, and 22. And for 200, its 38,39,40,41, and 42. I get it directly the first time I try it.

Ryan, age 7 of Westminster, MD wrote:
I knew I needed 5 numbers, so I divided 100 by 5 = 20. Then I used 2 up and 2 down. 19+21=40 22+18=40 40+40+20=100. I used the same technique for 200 and 300. The pattern is every 20.

Roshni, age 13 of London wrote:
At first I was pretty baffled! But then I realised it was obvious it was: 18+19+20+21+22= 100. It was very easy, but I found it challenging at first!

Indi, age 10 of Bozeman, MT wrote:
To find the sum of any five consecutive numbers, just take the middle number (3rd number) and multiply it by 5. So, if you want to find out the five consecutive numbers that add up to 300, just divide 300 by 5 and you get your middle number in the sequence- in this case it's 60. So, your five consecutive numbers are: 58, 59, 60, 61, 62.

Alex, age 14 of Rockford, IL wrote:
It is simple I figered that 9 and 1 would equal 10 and the same with 8 and 2. I also knew 20 times 5 would make 100. so I thought 19 and 21 would equal 40 witch is 20x2. The same with 18 and 22. so 18, 19, 20, 21, 22 is the answer. I tought and 20 to each # will equal 200 and the same with 300.

Marisa, age 10 of Brookings, SD wrote:
I got it 2 ways I did 18+19+20+21+22=100 and I did 9+10+11+12+13+14+15+16=100

Emily, age 12 of Eden Prairie, MN wrote:
I found the pattern. We are studying algebra now, so I solved it algebraically. x+x+1+x+2=100. Try it!

Zeeshan, age 13 of Plainsboro, NJ wrote:
I got the solution by using algebra. You set up an equation. Use the variable "x" to represent the first number. Then, since, the numbers are consecutive, use use x+1, then x+2, x+3, x+4 which represent the 1st, 2nd, 3rd, and 4th numbers, respectively. Then solve the equation x+x+1+x+2+x+3+x+4=100

Laura, age 14 of Mount Airy, MD wrote:
Since you are using 5 numbers, divide the startin number by 5. This will be the third number in the sequence. The other numbers are the two numbers before it and the two numbers after it. (If you are doing... lets say... 1200... 1200/5=240... so the 5 numbers are 238, 239, 240, 241, and 242... see?.. 240 is the middle number!)

Bethany, age 12 of Scottsville, NY wrote:
I relized that since we had to use 5 numbers that I should dived 100 by 5. I figered that was 20. So I gest to start with 18 because it was close to the number 20 and the numbers had to be consecutive. When I added it all up it came out to be 100. I was glad that I was right and I did the same thing with 200 I found it quite simple and I would love to do another one a littel bit harder.

Sarah, age 11 of Kanata, ON wrote:
I got that 18+19+20+21+22=100. It was really hard to figure out. It was really fun though!!! I just love a hard math challenge!

Alan, age 11 of Vancouver, AB wrote:
100=n+n+1+n+2+n+3+n+4 100= 5n+10 90=5n n= 18 Therefore 18 is the base number.

Carly, age 12 of Debert, NS wrote:
To equal 100 we used the numbers 18+19+20+21+22 that equaled 100. Then to equal 200 we just double the numbers we used to get the number 100 we also notice for numbers for 200 the went up by 2 and the numbers for 300 went up by 4.

Marie, age 12 of NS, Canada wrote:
We had to think a lot and then we figurd it out and it was 18+19+20+21+22 which = 100. First we thought it was wrong but it was realy wright cause we checked using the cumputer calatular. And we had lots of fun. You should do it again.

Tyler, age 14 of Lincoln, AR wrote:
I do not have any new results, but I do have an explenation for why that it worked the way you did it. You first divided the number by 5, then added a two to that, and went down five numbers from there. For example, 100/5=20, so the numbers are 22, 21, 20, 19, 18. The reason this is is that if you take the two off the 22 and add it to 18, you get 20 for both of those. That gives you 20, 21, 20, 19, 20. Then you just take the 1 off the 21 and add it to 19 and all of them are 20! and we know that 5x20=100, so there you have it! This always works if you want an odd number of consecutive numbers.

Jordan, age 9 of San Antonio, TX wrote:
I found the number 18, 19, 20, 21, 22 equal 100. My mom helped me but I guessed the numbers and used a calculator to prove that I was right.

Kasey, age 10 of Raleigh, NC wrote:
It is hard to figure out the right consecutive numbers. My grandmother and I figured out 7 numbers in 100. It is 9+10+11+12+13+14+15+16=100. I also have a question to ask: if you divide 6000 by 8 and you get 750 how many concecutive numbers will there be and can it happened???

Sarah, age 8 of Ypslanti, MI wrote:
At first I thought it was easy. But I was thing,"How in the world am I suppost to do this?"I thought and thought. Finaly I realised it was easy! 18+19+20+21+22=100! 28+29+30+31+32=100! And so on. Who would have thought it was so easy!

Sarah of Singapore wrote:
I almost laughed at the simplicity of the consecutive numbers. It is fun to work them out using the algebra method.

Madison, age 9 of Houston wrote:
It was hard but you add ten each time. 100=18 19 20 21 22. 200=28 29 30 31 32. 300=38 39 40 41 42.

Angel, age 11 of Gretna, LA wrote:
Each time, from 100, 200, and 300 you had to add 10 to the con. numbers. Example: 100=18, 19, 20, 21, 22; 200=28, 29, 30, 31, 32; 300=38, 39, 40, 41, 42.

Jenna, age 14 of Odessa, TX wrote:
I am an 8th grade algebra student so I know a shortcut to working this kind of problem. N stands for the number you are trying to find the value of so you use this equation: (n)+(n+1)+(n+2)+(n+3)+(n+4)=100. This is a very involved equation and may not work for you if you don't get it.

Divya, age 9 of West Nyack, OK wrote:
Me and my friend, Shimul tried this experiment at home. First, we divided 100 by 5. The answer was 20. So then, we played around with the numbers and found out that the consecutive numbers 18, 19, 20, 21, and 22 when added together equal 100.

Nokomis, age 12 of West Point, VA wrote:
When I used 7 consecutive numbers they equaled up to 98. The numbers I used were 11, 12, 13, 14, 15, 16 & 17. The experiment kind of confuse me, so I got help from my 16 year old sister.

Danielle, age 11 of De Soto, KS wrote:
I was estimating and I found that 18, 19, 20 all would have rounded to 20. 21, and 22 also rounded to 20. So I figured that if there were five numbers that all rounded to 20, I tolk 20x5. That equaled 100.

Akhil, age 6 of Montebello, CA wrote:
5 consecutive numbers for 100. Divide 100 by five then make the five numbers by going up and down. The numbers are 18, 19, 20, 21, 22.

not yet implemented