Numbers hide magic and mysteries. Read a little, then play. Clear all six games!
What it is
In a row of numbers, a supercell is a number that is bigger than the numbers on both sides of it.
Why it works
You simply compare each number with its left and right neighbour. If it beats both, it is a supercell; if a neighbour is bigger, it is not. An end number only has one neighbour to beat.
Why it matters
Spotting the biggest in a group quickly is useful, and it trains you to compare numbers with ease.
A few examples
In 3, 8, 5 the number 8 is a supercell, since 8 > 3 and 8 > 5. In 4, 2, 9 the 9 is a supercell.
What it is
From a set of digits you can build many numbers. The largest puts the biggest digit first; the smallest puts the smallest digit first.
Why it works
In our place value system the leftmost digit is worth the most, so a big digit on the left makes a big number, and a small digit on the left makes a small number.
Why it matters
It shows how place value decides a number's size, and it helps with rounding and comparing.
A few examples
From 3, 7, 1 the largest is 731 and the smallest is 137. From 6, 2, 8 the largest is 862.
What it is
A palindrome is a number that reads the same forwards and backwards, like 121 or 3443.
Why it works
The first digit matches the last, the second matches the second last, and so on to the middle. If every pair matches, it is a palindrome.
Why it matters
Palindromes make pretty patterns, and you can even build one by adding a number to its reverse.
A few examples
44, 232 and 1221 are palindromes. 123 is not, because backwards it reads 321.
What it is
Take any four-digit number with different digits. Arrange the digits biggest to smallest, then smallest to biggest, and subtract. Repeat, and you always reach 6174.
Why it works
Each subtraction pulls the number towards the same special value, and once you reach 6174 it stays there: 7641 − 1467 = 6174 again.
Why it matters
It is a famous discovery by the Indian mathematician D. R. Kaprekar, showing hidden order in ordinary subtraction.
A few examples
Start with 3524: 5432 − 2345 = 3087, then 8730 − 0378 = 8352, then 8532 − 2358 = 6174.
What it is
Pick any number. If it is even, halve it. If it is odd, multiply by 3 and add 1. Keep going and you always seem to reach 1.
Why it works
Even numbers shrink when halved, and odd numbers become even after 3n + 1, so the numbers keep bouncing until they fall down to 1.
Why it matters
No one has ever proved it always reaches 1, so this simple rule is a famous unsolved mystery in mathematics.
A few examples
Start at 6: 6 is even so 3, then 3 is odd so 10, then 5, 16, 8, 4, 2, 1.
What it is
To estimate is to find an answer that is close enough, quickly, without working out the exact value. We often round the numbers first.
Why it works
Rounding each number to a nearby ten or hundred makes the sum easy to do in your head, and the answer stays close to the true one.
Why it matters
Estimation helps you check whether an answer is sensible, and is handy for shopping, time and measuring.
A few examples
312 + 489 is about 300 + 500 = 800. 47 × 9 is about 50 × 9 = 450.
Have a go on paper first, then tap to see the clear steps.
Q1. In the row 4, 9, 2, which number is a supercell?
Q2. What is the largest number you can make from the digits 6, 2, 8?
Q3. Is 252 a palindrome?
Q4. Kaprekar step: arrange 3524 as 5432 and 2345, then subtract.
Q5. Apply the Collatz rule to 5.
Q6. Estimate 288 + 512 by rounding to the nearest hundred.