Six math riddles with answers (and why you'll get the first one wrong)
Six classic math riddles with the answer explained step by step. Almost all of them share the same trick: the answer that pops into your head first is the wrong one, and there's a known reason for that.
A good math riddle isn't hard to calculate. It's hard to frame. You can spot one because the answer arrives on its own within two seconds, with a comfortable feeling of obviousness... and it's wrong.
Here are six. All of them are primary-school arithmetic: if you get one wrong, it won't be the maths. The answers are at the end, so you can think them through first.
1. The bat and the ball
A bat and a ball cost $1.10 together. The bat costs $1 more than the ball.
How much does the ball cost?
2. The machines
If 5 machines take 5 minutes to make 5 widgets...
how long would 100 machines take to make 100 widgets?
3. The lily pond
Lilies grow on a pond and double in area every day. They take 48 days to cover the whole pond.
How many days do they take to cover half of it?
4. The snail in the well
A snail is at the bottom of a 10-metre well. Every day it climbs 3 metres, and every night, while it sleeps, it slides back 2 metres.
How many days does it take to get out?
5. The seventeen camels
A man dies leaving 17 camels to his three sons, with these instructions: half to the eldest, a third to the middle son and a ninth to the youngest.
Seventeen can't be halved without killing a camel. A neighbour turns up with one camel and solves it without any animal being harmed and without keeping anything.
How?
6. The missing dollar
Three friends have lunch and the bill is $30: they put in $10 each. The waiter realises the bill was actually $25 and comes back with $5 change. Since $5 doesn't split three ways, they each keep $1 and leave him $2 as a tip.
So: each of them has paid $9, and 9 × 3 = $27. Plus the $2 tip makes $29.
Where's the missing dollar?
The answers
1. The ball costs 5 cents
Not 10. If the ball cost 10, the bat would cost 1.10 and the total would be $1.20.
With the ball at 0.05, the bat costs 1.05 and the total is 1.10. ✔
The mistake has a name: you subtracted $1 from $1.10 and kept what was left over. But the puzzle doesn't say the bat costs $1, it says it costs a dollar more than the ball, and that difference is split between the two of them.
This riddle was popularised by the psychologist Daniel Kahneman precisely because more than half of students at elite universities answer 10 cents. It isn't a question of mathematical ability.
2. Five minutes
If 5 machines make 5 widgets in 5 minutes, then each machine makes one widget in five minutes. That's the figure you have to extract.
100 machines working in parallel make 100 widgets in those same 5 minutes. Adding machines doesn't stretch anything out.
The automatic answer, 100 minutes, comes from multiplying instead of looking at the rate per machine.
3. Day 47
If day 48 is full and each day doubles the day before, the previous day must have been exactly half.
What's interesting is what that implies: on day 40 the pond is only 0.4 % covered. Eight days before disaster, you can't see anything. It's the best intuitive description of exponential growth there is, which is why this riddle gets used to explain epidemics, compound interest and debt.
4. Eight days
The trap is to reason "it climbs 3, drops 2, so it gains 1 metre a day, therefore 10 days".
That fails because the last climb has no night after it. The snail is already out, so it doesn't slide back.
The real count: at the end of day 7 it's at 7 metres. On day 8 it climbs 3, reaches 10 and leaves. Eight days.
5. You borrow the camel and give it back
With the neighbour's camel there are 18:
- Half of 18 → 9 camels for the eldest
- A third of 18 → 6 for the middle son
- A ninth of 18 → 2 for the youngest
9 + 6 + 2 = 17. One is left over, which is the neighbour's, and he takes it home.
Why does it work? Because the father's division never added up to one: 1/2 + 1/3 + 1/9 = 17/18. He never divided the whole thing, he left an eighteenth out. The borrowed camel only serves to make that gap visible.
6. No dollar is missing. The question is malformed
The $27 they paid already includes the $2 tip. Adding it again counts it twice.
The correct sum:
$25 (food) + $2 (tip) + $3 (returned) = $30 ✔
Or the other way round: $27 paid = $25 of food + $2 of tip.
This riddle isn't a maths problem, it's a wording problem. And that's the most useful lesson of the six: when a figure doesn't add up, quite often it isn't your arithmetic that's wrong, it's the question.
The pattern the six share
In five of the six, the wrong answer arrives before the right one and arrives with a feeling of certainty. That isn't carelessness: it's how the mind works. You have a fast system that answers by pattern recognition and a slow one that calculates, and the fast one answers first.
The only practical defence is a habit: when the answer looks obvious, check it. With the bat and the ball, checking takes five seconds and saves you.
How to train it
Trick riddles run out: once you know the lily pond, you know it forever. What doesn't run out is what sits underneath — handling numbers fluently and reading a problem with suspicion.
That's trained with short, varied bursts: mental math tricks for fluency with numbers, number sequences for patterns and logic puzzles for tricky wording.
In MenteBrillante they're spread across Quick Maths, Logic Sequence and Riddle, with five new challenges every day. You can try them in the web version.