How many turns?

Number Theory Level 2

We start with the number 999. You can choose to remove 1 digit from the number, subtract 5, or divide by 2. What is the least amount of moves it can take to make 1?

You cannot make non-integer values.

4 8 9 3 5 7 10 6

2 solutions

A Former Brilliant Member
Jul 22, 2020

Our goal is to try to make 999 into 1 with the choices provided.

Our first goal is to get it to a 1 digit number. Thankfully, using the remove 1 digit choice 2 times gets us 9.

Then, looking at our other choices, we can only subtract 5, so we get 4.

Then we divide by 2 2 times to get 1.

Counting our moves, we get 2+1+2= $\boxed{5}$

So if we had started at $n=5$ instead of $n=999$ , we'd be stuck. Are there any other numbers that we can't get to $1$ from with this algorithm?

Chris Lewis - 10 months, 3 weeks ago

Mahdi Raza
Aug 1, 2020

Step 1: Remove any one digit

$999 \rightarrow 99$

Step 2: Again remove any one digit

$99 \rightarrow 9$

Step 3: Subtract 5

$9-5 \rightarrow 4$

Step 4: Divide by two

$4\div2 \rightarrow 2$

Step 5: Divide by two

$2 \div 2 \rightarrow \boxed{1}$

How many turns?

2 solutions

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