## Induction puzzles from the 2003 World Puzzle Championship

The vast majority of the problems in the World Puzzle Championship are of the same ilk as from the most recent championship in Turkey. Every once in a while an induction puzzle sneaks on, the kind where one looks for a pattern and guesses the rule or fills in the missing pieces.

I’ve had these puzzles lurking about since the 2003 championship in the Netherlands occurred, and I’ve never been able to solve four of them. I figure at seven years old it is high time to get them off my queue.

First off, a set called Common Touch based off of Bongard problems. I know the answers to only the first two.

In each of the three puzzles, 4 puzzlers in the YES group all share an unusual property, which none of the names in the NO group have. For each puzzle, pick one of the 8 names from the answer list that shares the property in the YES group. Note that the answers have nothing to do with the people themselves, only the names.

Puzzle 1:

YES: LASLO MERO, CLAUDE DESSET, NECMIYE OZAY, ANDREAS BOLOTA

NO: KAROLY KRESZ, METIN BALCI, PAVEL KALHOUS, ROGER BARKAN

Puzzle 2:

YES: CLAUDE DESSET, NIELS ROEST, LASZLO OSVALT, ANNICK WEYZIG

NO: DAVID SAMUEL, DELIA KEETMAN, TETSUYA NISHIO, RON OSHER

Puzzle 3:

YES: PETR NEPOVIM, BIRGIT ROSENTHAL, PAVEL KALHOUS, DARIUSZ GRABOWSKI

NO: TIM PEETERS, HUSNU SINCAR, ALEXANDRU SZOKE, EMERIC LORINCZ

Answer list: JOHN WETMILLER, JAN LAM, HANS EENDEBAK, ULRICH VOIGT, ZACK BUTLER, JAN FARKAS, ROBERT BABILON, SILKE RITTER

Out of these “fill in the question mark” problems, I have solved exactly zero:

### 7 Responses

1. My god man! It’s like you’ve been sent from a rival school to prevent me from EVER entering in grades. I’ve already got enough procrastination time with the World Chess Championship going on. How much can I possibly geek out in one 24 hour period?

2. So do you have the answers, or any way to tell if we come up with answers if they are right or not?

SPOILER-Potential
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Like that’s going to help…

Ok, the first of the number square problems seems to be this:
The four outer boxes (I started calling them petals) bear a relation to the center number as follows:
First flower: the center is the difference of the differences of opposing petals. (12-9)-(17-16)=3-1=2
Second flower: the center is the difference of the sums of opposing petals. (22+10)-(7+15)=32-22=10
Third Flower: The center is the sum of the differences of opposing petals. (13-12)+(21-18)=1+3=4
By induction, I’m guessing that the last flower’s center is the sum of the opposing petals’ sums, (11+14)+(19+26)= 25+45=70.
or else it isn’t.

• Thanks for posting!

I think it’s simply “the center is difference of the sum of the evens and the sum of the odds”. Someone messaged me that answer, but I don’t know the answers to the others (except the first two). That’s why I was asking.

3. The second of the three numbers puzzles:

Middle = 2*(top – (bottom+left+right)), giving an answer of 2.

(TripleM via caravelgames)

• Wow … I don’t feel bad about not getting these now.

Still the third and sixth puzzles outstanding, I might poke my head in a few different forums to see if anyone has an idea.

• Well, I do have a possible answer for the last one. Seems a little contrived, and with these types of puzzles you’re never really sure if you have the right answer or not..

If you add top and left, and bottom and right for each group:

7,11, 4,11, and 8,12

If you add their reverses, you get the reverse of the middle number.