# Ning Nang Nong Latin square

My son is obsessed with the Spike Milligan nonsense poem ‘On the Ning Nang Nong’. Here’s a video of Spike reciting it.

This weekend, he asked me to help him learn it. I’ve tried to memorise it before, to save having to find the book when he wants me to recite it. But somehow, it’s never quite stuck. I can remember all the bits and the basic order (Cows-Trees-Mice), and know what happens after the lines ending “Nong” (“Cows go bong”), “Ning” (“Trees go ping”) and “Nang” (“Mice go clang”). What I struggle with is remembering which order the “Ning”, “Nang” and “Nong” go before the one that rhymes with what comes next.

At the weekend, I wrote “Ning”, “Nang” and “Nong” on pieces of paper and we rearranged them as we read the poem. I realised my difficulty is a mathematician pattern-spotting one. There’s a not-quite Latin square embedded in the poem.

There are six permutations of the words “Ning”, “Nang” and “Nong”.

1. Ning Nang Nong
2. Ning Nong Nang
3. Nang Nong Ning
4. Nang Ning Nong
5. Nong Ning Nang
6. Nong Nang Ning

The poem uses three of these (1, 5 and 6 in the list above). I think my problem is that although all possible endings are used, the same is not true of the starting positions. This is why I struggle to remember whether it is the one that rhymes with “Trees go ping” or the one that rhymes with “Mice go clang” that starts “Nong”. I’m expecting variety, but actually both start with “Nong”.

That is to say, the choice of three permutations doesn’t form a Latin square. And it could. Here is a Ning Nang Nong Latin square:

 Ning Nang Nong Nang Nong Ning Nong Ning Nang

I think I would find the poem more pleasing, and easier to remember, if this structure were embedded. Still, realising this is my problem seems to have helped – I can now remember which lines go in which order.

My son has adapted the final line of the poem. It goes “What a noisy place to belong, is the Ning Nang Ning Nang Nong”. He then shouts “And here!”

With all this Ninging, Nanging and Nonging, he’s not wrong.