Cubes and dice

Story hook

It is Sunday afternoon. Little Ananya has a big block of chocolate — one of those thick, square ones. Her father takes a knife and slices it into many small chocolate cubes, all the same size, like tiny dice. Now there is a neat pile of little chocolate cubes on the plate.

Then her father plays a game. "Imagine," he says, "that before I cut it, I had painted the whole outside of the big chocolate block with colour. Now look at the small cubes. Some of them would have colour on three sides. Some on two sides. Some on only one side. And a few — the ones hiding right in the middle — would have no colour at all, because the knife only reached them after cutting."

Ananya frowns. "How can you know how many have three colours, or two, or none, without checking every single one?"

Her father smiles. "There is a little secret. Once you know it, you can count them all in your head — even for a giant block cut into a thousand pieces."

That little secret is exactly what this lesson teaches. We will also learn the friendly secret of an ordinary dice (the cube with dots you roll in games like Ludo and Snakes-and-Ladders). By the end, painted cubes and dice will feel like an easy puzzle you can win every time.

Why this matters for UPSC

CSAT is Paper II of the UPSC Prelims, and it is a qualifying paper. That means you do not need a huge score — you only need 33% to pass (about 66 marks out of 200). So the smart plan in CSAT is to grab the easy, quick marks first. Cube-and-dice questions are exactly that kind of quick, safe mark. Once you know the three or four small rules in this lesson, most of these questions take well under a minute and need almost no calculation.

In real life this topic is everywhere too. Every dice game you play (Ludo, Snakes and Ladders, board games) uses the dice rules you will learn here. A Rubik's cube — that famous colourful puzzle — is just a 3-by-3 painted cube, so the painted-cube counting is literally describing a Rubik's cube. Even packing boxes, stacking sugar cubes, or building with blocks uses the same picture-in-your-head skill. So this lesson sharpens your exam brain and your everyday brain at the same time. Go slowly, draw little pictures, and you will find it is genuinely fun.