Kjarposko

[hopeful traveller]

(I don't know if these have a proper name, and I'd be rather surprised if they don't, but...)

The Benjamin's Blog's mathematicians at Benjamin's Blog headquarters had spent so much time doing Sudoku, Kakuros, and analysing election results in Harrow-on-the-Hill that one day they decided to get their revenge. They locked to the door, grabbed some shapes, lines, and numbers, and performed some ghastly experiments on them, until, suddenly, one day, they had at last created something with which they could frustrate the world, and, just to make things worse, they gave it the most ridiculous name in the world: the Kjarposko.

It involves a selection of boxes which are linked together. Each box is divided into two sections - there is a number on top and a space underneath.

There's only two rules: every number on top of a box equals the total of the answers in the bottom of the box linked to it and no number may be used more than once. (A list of numbers you may use will be provided).

Confused? Don't panic. Let me guide you through an example.



You need to put 1, 2, and 3 into the three boxes. The box with 4 in it is linked to the boxes with the 3 on top and the 5 on top. Therefore, the numbers you put into the '3' and '5' box must add up to 4. In the same way '3' + '4' = 5 and '4' + '5' = 3.

Righty-ho, then:

I suggest fitting a smoke detector to your head to attempt these.




BRAIN TEMPERATURE: NORMAL







BRAIN TEMPERATURE: HOT







BRAIN TEMPERATURE: SIZZLING







BRAIN TEMPERATURE: CRITICAL







BRAIN TEMPERATURE: TOO HOT FOR WORDS







WARNING

You are now approaching one of the most lethal puzzles on the planet. It is so hard that it is on the edge of meltdown and some of the numbers have evaporated into * symbols. It is still possible to fill in the answers, but if you are of a nervous disposition DO NOT ATTEMPT THIS PUZZLE.

BRAIN TEMPERATURE: EXPLODED





(OK, I'll admit it, I got it out of a book.)

[Iain]

3 + 4 = 5??

The book you got these from, is it the Gideon Osbourne book of mathematics?

[Iain]

Joking apart, these look rather fun, although at first glance through beer goggles it's a series of simultaneous equations.

[The Orange One]

Sizzling is impossible. It's mathematically impossible. I can prove why.

Let the "20" box be x. Then the "18" box is 5-x. Then the "22" box is 6-(5-x)=1+x. Then the "25" box is 14-(1+x)=13-x. Then the "17" box is 14-(13-x)=1+x. Then the "20" box is 8-(1+x)=7-x.

So x=7-x
2x=7
x=3.5 - just thought I'd let you know.

[hopeful traveller]

3 + 4 = 5??

The book you got these from, is it the Gideon Osbourne book of mathematics?

No, the book uses letters in the example, but I thought that would be far too complicated to understand. Hence I used '3' rather than 3 to indicate that it's not the number 3, like putting ' in front of a number in Excel.

[Iain]

Ah so in that sense '3' means the number at the bottom of the box with 3 at the top?

[hopeful traveller]

Ah so in that sense '3' means the number at the bottom of the box with 3 at the top?

Come again?

By '3', I mean 'the box with 3 on top'. So... the three box + the four box = 5.

[Iain]

Yes, that's what I meant

[tubeguru]

Well at least this is a nice easy puzzle that everyone can pick up ...

[GuyBarry]

(I don't know if these have a proper name, and I'd be rather surprised if they don't, but...)

Named after Kjartan Poskitt, who invented them. See http://puzzles.wikia.com/wiki/Kjarposko

Sizzling is impossible. It's mathematically impossible. I can prove why.

Let the "20" box be x. Then the "18" box is 5-x. Then the "22" box is 6-(5-x)=1+x.

OK so far (assuming you mean the lower of the two "22" boxes).

Then the "25" box is 14-(1+x)=13-x.

I think you've slipped up here. The "25" box is connected to the two "14" boxes. The "1+x" is in the "22" box, which is not connected to the "25" box.

By the way, the "lethal" one isn't really that lethal - I've just solved it in about 20 minutes. (Haven't tried the others yet.)

[The Orange One]

Yes but the box in the lower "22" and the "25" are the only boxes connected to the lower "14". So they must both sum to 14.

(hopeful traveller showed me the solution - there is, in fact, an error inside it)

[DrainBrain]

I don't get the Sizzling one:

To make the "5" box correct, the highest number that can go in the "20" box is 4, but that immediately makes the middle "22" box impossible. Am I missing something? (Or are there connecting lines missing, or maybe the numbers are wrong?)

[The Orange One]

Yeah there's horrible problems with the Sizzling one.