## Thursday, April 7, 2011

### Eight eights that are a thousand

This is an easy puzzle that you all are welcome to share with your kids and friends:
Put addition signs between the digits 88888888 to get 1000.

Answers accepted all day long on Friday April 8th, on our Family Puzzle Marathon. They will be hidden until Saturday morning (EST) and everyone who solved it will get a puzzle point. Please, explain your answer.

Dennis (of Dennis and Katrina) said...

To make 1000, the ones digit has to add up to something ending in a zero. That's 40, which means "88888888" will need to be divided into 5 numbers.

When you add the ones digits to 40, you'll need to carry the 4 into the tens place. The tens place will also need to add to something ending in a zero to make 1000. With carrying the 4, you'll need two 8's to make 16.

Now you'll need to carry a 2; add an "8" to that, and you'll get 10, which looks a lot like the start of 1000. Let's see where we are - we need five numbers with a ones digit, two with a tens digit, and one with a hundreds digit. This gives us 888+88+8+8+8, or 1000!

thelittlebird said...

888 + 88 + 8 + 8 + 8 = 1,000

Start by using the largest number that gets you close to 1,000. Add your second largest number to get you within range so that your single digits will bring you to your goal.

This is a good comparison to how I'm teaching my daughter to make change. She initially started by randomly adding different coins until she got the right amount and we talked about how efficiency in making change is important. We discussed starting with the largest bill needed and gradually decreasing in bill or coin amount to get to the goal.

Have a great weekend!

Unknown said...

This is a quick and fun one...

=8+8+8+88+888 = 1000

anne-marie said...

888+88+8+8+8

Wang said...

888 + 88 + 8 + 8 + 8 = 1000

The trick is to realize that there must be at least 5 'parts' because that way the sum will have a '0' at the end.

kj said...

8 + 8 + 8 + 88 + 888 = 1000

First we see that there must be five terms, since 8 * 5 = 40 is the smallest multiple of eight that is divisible by ten. We also determine that one of the terms must be 888, since 8888 will put us over 1000, and adding together eights and eighty-eights will never get us to 1000 with only eight eights to work with.

1000 - 888 = 112, and we have five eights left, so we must use two eights for 88, leaving us with three eights.

112 - 88 = 24 = 3 * 8 = 8 + 8 + 8, so we are done.

8 + 8 + 8 + 88 + 888 = 1000, which has the requisite five terms.

Another way to look at it is going back to the first assertion that there must be five terms. That leaves three eights to place, and the only possible combinations are:
8888 + 8 + 8 + 8 + 8 = 8920 (place all remaining eights in the first term)
888 + 88 + 8 + 8 + 8 = 1000 (place all remaining eights in the first and second terms)
88 + 88 + 88 + 8 + 8 = 280 (place all remaining eights in the first, second and third terms)

PApaige said...

8+8+8+88+888 = 1000. I took this into a 3rd grade class for some Friday morning math fun. Thanks!

SteveGoodman18 said...

1000 = 888 + 88 + 8 + 8 + 8

There are 20 different orderings in which this sum could be written. Since there are 5 terms in the sum, there are 5 choices for where the 888 would go, and then 4 remaining choices for the 88. The three remaining terms are then automatically the single digit 8's.

tom said...

tom says
8888 / 8.888 = 1,000

Lynnet said...

888+88+8+8+8=1000

Donna said...

Since I know that 125 x 8 equals 1000, 888 = 111 8's, so I would still need 14 more. 88 equals 11 8's, and because I would only need 3 more 8's, that uses all 8 8's. i.e. 888+88+8+8+8 = 1000.

Bean said...

888 + 88 + 8.+ 8 + 8

Anonymous said...

I feel a little guilty getting a puzzle point for this but here goes.
888 + 88 + 8 + 8 + 8 = 1000.
I then took a another look at it to see if there was another way to solve it. Since all the digits are 8, the only way to get 8s to sum to 1000 or any other number that has a 0 in the ones column, is to to have five 8s in the ones place. And the only way to get five numbers with an 8 in the ones place is to add a three digit # plus a two digit # + one digit # + one digit number + one digit #.

Mathmover

Annie said...

888 + 88 + 8 + 8 + 8 = 1000

Maria said...

Almost all of you did it! A rain of puzzle points for: Dennis, thelittlebird, Carrie, anne-marie, Wang, kj, PApaige, SteveGoodman18, Lynnet, Donna, Bean, mathmover, Annie.

Thank you for those who explained their reasoning.

Tom - we love you. You are so special. But this was an addition puzzle :)

Tom said...

jt1250champion said...

easy 888+88+8+8+8
but shouldnt you block other answers cause people can just copy
the way i did this was 1000must end in 0.8 times 5 =40. highest numberhere would be 888 without going over.5 8s left for 4 spaces so 88,8,8,8.

bengm37 said...

(8888-888)/8 = 1000

Anonymous said...

8*8+8*8*8-(8+8+8) = 64+64*8-24=128*8-24=1024-24=1000

Unknown said...

this is incorrect as BODMAS was not followed. multiplication should be first and then additon

vinoo cameron said...

The root is 2

(222+222+222+222)+(22+22+22+22)+(22)+(2)=1000

(888)+(88)+8+8+8=1000

The reason is simply that 8+2=10, and since 2^3=8, the combinations are infinite

Unknown said...

Guys there are 32 ways to get the answer as 1000. can anyone find that

Unknown said...

(8(8(8+8)-(8+8)/8))-8

ilyas2009 said...

Can anyone solve this one:
Eleven eights that are a thousand