# Tag Info

Accepted

### Make 0 0 0 0 = 8

I think that This is because This works and is valid because
Accepted

### Nine gangsters and a gold bar

18 pieces: In 9 parts: In 8 parts: In 7 parts: We need to be able to split it into 9 parts of 56, so it can't hurt to make 9 pieces of 56 and then split those further. Since we need to do better ...

because

### Make 0 0 0 0 = 8

Lateral thinking!
Accepted

### Make 5 5 5 5 = 19

Here's one way I found: Or, using just the characters explicitly allowed in the question:
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### The largest Monday number

Notice 9867312 is a Monday number. The largest Monday number may not contain 5 because in this case it would end in 5, and thus not be divisible by 2, 4 and 8, so it would have at most 6 digits. On ...

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 ...

### 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 ...

let me try:

### 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

It's different:
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### Professor Halfbrain and the sum of the digits of all divisors

Professor Halfbrain's theorem is Proof

### 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.

Evaluation:

### 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 ...

### Make 6 5 4 3 = 81

My solution: Just normal Math
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 ...

### Make 5 5 5 5 = 19

For the 5s For the 1s (previous edit)
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### Shifting a digit from right to left

I think the answer is Proof Computer check

### Nine gangsters and a gold bar

It has been shown that fewer than 16 pieces is not possible (due to the 8-way split then requiring someone to have a single piece larger than a single portion of the 9-way split). I'll show by ...

### Nine gangsters and a gold bar

22 pieces Suppose the weight of the bar is 504. I chose 504 since 7*8*9=504, so, the numbers would be easy to work with. 7 pieces of weight 56 (A) 8 pieces of weight 7 (B) 6 pieces of weight 9 (C) ...
Accepted

Step 1: Step 2:
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### 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 ...