On Friday I set this puzzle….

Can you use the same digit eight times with ‘+’ signs to produce a total of 1000?

If you have not tried to solve it, have a go now. For everyone else the answer is after the break.

One answer is…888+88+8+8+8=1000

Did you come up with any other answers?

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called **PUZZLED** and is available for the **Kindle** (UK here and USA here) and on the **iBookstore** (UK here in the USA here). You can try 101 of the puzzles for free here.

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Got it! But, in Base 2, 1+1+1+1+1+1+1+1=1000. No?

Yes, got the two solutions too. “Base 2″? I just call that binairy…

Mervulon

Isn’t your answer 255 in binary?

My answer too… @Anon — 255 isn’t a binary number :-)

Repton

I meant that Mervulon’s answer is the binary equivalent of 255 to base 10.

Sorry for the confusion.

@anon: no.

255 is 11111111 in binary.

1

10

11

100

101

110

111

1000 ( = 1+1+1+1+1+1+1+1)

8 in decimal.

I have the asnwer to next Friday’s quiz if anyone is interested:

“A bottle of baby oil and an ostrich feather”

You say tomato and I spell “binary” correctly.

I’ve been a thicky this week. I gave up, but its a great problem.

I would have thought the answer would be either YES of NO. Richard’s example would tend to YES as being the answer that is best to defend…

Repton

I meant that Mervulon’s answer is the binary equivalent of 255 to base 10.

Sorry for the confusion.

Anon

For the avoidance of doubt:

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 8 = 1000 in binary :-)

Remind me to invite you to my next party, just in case people start having too much fun.

Given the 8s answer was pretty trivial I like the binary solution because of the ‘out of the box’ thinking. Along similar lines we also came up with “1111 – 111″ where the “-” is made by turning a 1 on its side.

If you want out of the box thinking, I took eight match sticks and arranged two of them as the “+” symbol. The other six sticks (all of which were I the roman numeral for one) and arranged them as two triangles to serve as D’s making 500+500.

Pretty crap really but I was bored!

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and 13 1s can be arranged like matchsticks to ‘write’ 1000

I didn’t come up with the solution immediately because I started with 1 and moved upwards.

I came across a way to make a 1000 with 9 fourths like that:

4^4 + 44 + 4^4 + 444 = 300 + 700 = 1000

I got your “solution” MaciejK .

I also got yours Stevie – I thought it was a bit of a fiddle, albeit no worse than some of RW’s answers.

How many other numbers can be made by applying this rule? What about if we allow the number of digits to vary? Are there some ‘prime’ numbers that can only be generated by a long string of 1+1+1+1+… ? It feels like there is something interesting lurking just below the surface here.

888+88+8+8+8=1000

That’s all I could come up with, and that stretched me!

easy mode.

Assuming base 10..

There can be a maximum of 8 terms in the sum (and there have to be fewer). The number of terms in the sum multiplied by the chosen digit has to end in a zero. By ‘inspection’ of multiplication tables this gives 2, 4, 5 and 8 as candidates. First term in sum pretty well has to be three digit. Easy to eliminate 2, 4 and 5. Hence 8.

Another solution is

888 + (888 + 8) / 8

Nope, that’s obviously cheating.

Remind me to invite you to my next brainstorming session, just in case people start having too many good ideas.

@Vic

Thats not a solution at all, as the only mathematical symbols allowed was +

(1111-111)^1

What part of ‘+ signs’ is so confusing? Not ^. Not /. Not (). You got it, or you didn’t. Oh. And you didn’t.

Caret is only needed for exponents if you’re forced to write in one dimension.

I got the 8s solution but first I came up wit D+D+D+D+D+D+D+D=M(1000)

I got it in about 15 seconds in my head but I have to admit to inadvertantly getting a head start as I misread the question as “how can you use the number 8,eight times with + to get 1000″ It made for an easy puzzle!

Like mikekoz68’s result!

10+10+10+14+14+14+14+14=100 and uses the digit ‘1’ 8 times

didn’t say I couldn’t use other digits