# Tag Info

• 1,331
Accepted

### Make 0 0 0 0 = 8

I think that This is because This works and is valid because
• 32.3k

because
• 757

### Make 0 0 0 0 = 8

Lateral thinking!
• 3,614
Accepted

### Make 5 5 5 5 = 19

Here's one way I found: Or, using just the characters explicitly allowed in the question:
• 14.5k

• 3,197

### x⌊x⌊x⌊x⌋⌋⌋ = 2020

Observations to give lower and upper bounds: So we know for sure Now the whole thing becomes Contradiction ... and now I realise my implicit assumption that Going back to those two observations at ...
• 117k
Accepted

### First digit of 3^2020

I think it's a Explanation: According to my calculator (this answer was posted before the no-computers tag was added), If we're not allowed to use computers, I would The same trick is used to ...
• 28.1k

let me try:
• 3,828

### Make 5 5 5 5 = 19

If the double factorial is allowed, then I propose WolframAlpha agrees that the result is 19.
Accepted

### Make 6 5 4 3 = 81

I thought a bit too much but I finally got it:

### First digit of 3^2020

This is one way to do it with the help of binary numbers. It is called exponentiation by squaring. EDIT Thanks to the few comments that pointed out the mistakes in my calculations. I was very lucky to ...
Accepted

• 11.3k

It's different:
• 35.6k
Accepted

### Professor Halfbrain and the sum of the digits of all divisors

Professor Halfbrain's theorem is Proof
• 137k

### Make 5 5 5 5 = 19

I am quite sure it is not the expected answer but it is the immediate answer comes into my mind.
• 321

Evaluation:
• 5,181
Accepted

### What makes this polynomial a square number?

Of course, $x=0$ is an answer, so let's look for non-zero ones from now on. If the given expression is a perfect square, so is Now we try to estimate it by "nearby" perfect squares. One ...
• 19.6k

### Make 6 5 4 3 = 81

My solution: Just normal Math
• 301
Accepted

### Shifting a digit from right to left

I think the answer is Proof Computer check
• 137k

### Number of divisors equals square root

The number of positive divisors is a multiplicative function in the number theoretical sense. The square root is also multiplicative. We can therefore proceed prime factor by prime factor. If ...
• 21.3k

### Make 5 5 5 5 = 19

For the 5s For the 1s (previous edit)
• 3,197
Accepted

Step 1: Step 2:
• 5,948
Accepted

### What number follows up next? Part 2

OEIS doesn't list this sequence. After analyzing the pattern, I come to the conclusion that (one) answer is Explanation: EDIT (05/06/18): I submitted this sequence to OEIS and it has (finally) been ...
• 1,370

### Nice no-computers way to find limerick primes?

Obviously a is one of {1,3,7,9} and a,b are coprime. Also, b can't be a multiple of 3 regardless (else our number is a multiple of 3). That leaves 23 possibilities (4 for a, 6 for b, but we can't have ...
• 120k

### How to find the 2021st integer co-prime to 15

The trick is this:
• 147k
Accepted

### Professor Halfbrain and numbers with many zeros

The Professor is: Because:
• 9,431
Accepted

### Fun with numbers: solve A to E

Explanation: Recap to see that all of them fit:
• 18.2k
Accepted

### Consecutive integers around a circle

I have a solution using 448 consecutive integers. The integers are centered on a number which I will call $c$, which is: ...
• 7,148