# Answer to the Friday Puzzle….

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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.

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.

1. Mervulon says:

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

• -M- says:

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

• Anon says:

Mervulon

• repton says:

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

• Anon says:

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

• -M- says:

@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.

• Hugh Janus says:

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

“A bottle of baby oil and an ostrich feather”

• Mervulon says:

You say tomato and I spell “binary” correctly.

2. Indy says:

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

3. Roland says:

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…

4. Anon says:

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

• Eddie says:

Anon
For the avoidance of doubt:
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 8 = 1000 in binary :-)

• Dave says:

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

5. Ken Zetie says:

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.

• Stevie says:

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!

• Martha says:

Like

• Lazy T says:

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

6. MaciejK says:

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.

7. SimonP says:

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.

8. PJR says:

888+88+8+8+8=1000

• PJR says:

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

9. Match says:

easy mode.

10. Anonymous says:

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.

11. Vic says:

Another solution is
888 + (888 + 8) / 8

• Dave says:

Nope, that’s obviously cheating.

• Eddie says:

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

• mikekoz68 says:

@Vic

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

12. Anonymous says:

(1111-111)^1

13. Mervulon says:

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

• Anonymous says:

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

14. Mark says:

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

15. mikekoz68 says:

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!

• Karen says:

Like mikekoz68’s result!

16. lmiyar says:

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