We have written about Tony Gardiner and excerpted from his writings a number of times: here, here, here, here and here. We will post an entire article by Tony in a day or so, but we are first posting the problems contained within the article. Unlike the “problem” here, the problems below are genuinely presented by Tony to puzzle over, and are only loosely tied to the text of the article. Have fun.

These are brilliant. Love them.

Still thinking about C part (b) and E.

Won’t post my answers to the other problems; I think problem D is pretty clever for a few reasons.

C(b): No. There are 25 pairs and the maximum sum of a pair is 50+49=99. There are only 25 primes less than 99 and one of them is 2, which is unobtainable.

E: {8,9,10,12}

Thanks. Can you solve C(a)?

That (C(a)) wasn’t as difficult as it first appeared. Will hold off posting my solution to allow others to ponder.

E has me thinking still – yes there exists a set of 4 such numbers, but 5 or 6…? Or a different set of 4…?

I feel I’m missing something though… and I love it!

D I think would have been difficult if I hadn’t thought of the answer straight away by considering two tetrahedrons stuck together.

Yes, E seems to me very interesting.

Marti,

Nice puzzles. My favourite from year 7 was identify the counterfeit coin in a dozen identical coins given a traditional two pan balance and 3 weighings and also whether the fake was heavier or lighter than the rest .

PS perhaps now is the time to share some of Martin Gardner’s articles in Scientific American from the 70s a sample of NOTCHES are here https://static.scientificamerican.com/sciam/assets/media/pdf/Aug2008_Martin_Gardner_Recreational_Mathematics.pdf

Steve R