‘I’m really sorry, Manali,’ said Himani. ‘My mother’s upstairs making a work call, so we have to stay here and look after Chhotu. We can’t go to the shops until she’s finished.’

‘That’s okay,’ said Manali. Himani’s little brother, Chhotu, though two and a half years old, is fairly easy-going.

‘We’ve got the buttons out. He loves playing with them,’ said Himani. The carpet was covered with patterns of red and white buttons.

Manali looked closer and said, with awe in her voice, ‘I think Chhotu has made sequences. Look at the cross pattern. There’s a red button in the middle, and a white button above and below, and left and right. The next pattern has got two white buttons above, below, left and right, and the third has got three in those positions.’

Himani giggled. ‘He’s clever, but he’s not that clever! I made those patterns – he just picked the colours.’

‘In that case, I’ll make a sequence!’ Manali placed two red buttons, one above the other. Then she put one button on the right of the top button, and one button to the left of the lower button. She carried on, until her sequence was 4 buttons, 6 buttons, 8 buttons and so on.

Manali was finishing another sequence with position rule 5 + 3n (n ≥ 0), when Himani shouted, ‘No, Chhotu! You can’t eat buttons!’ She dived towards Chhotu and grabbed back the buttons he was holding near his mouth. ‘Phew!’ said Manali. ‘No one should love buttons that much!’