# Some puzzles suggested by searchers

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Puzzle solvers, try your hand at these. I looked at some search strings from people wandering in here looking for answers, and tried to guess what puzzles the searchers were trying to find solutions to.

1. *Math puzzle Combine 1, 5, 6, 7 to make*… I assume 24? I don’t see an answer. Other puzzlers? Do you think using factorial should be allowed? (then I’ve got 7!/[5(6+1)] )

2. *All factors of 90*: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. You could divide each number, 1 through 9 into 90, and then include it if it goes in evenly, and then ‘partner’ each of those factors with a larger one: 90/9 = 10, 90/6 = 15 , and so on. Or you could note that 90 = 2^{1}3^{2}5^{1} and review the logic in this post.

3. *Distance formula puzzle*. Oh, there are lots of those. I like this one: How far is it as the crow flies from the front upper left corner of a 10x10x10 room to the back lower right corner? Make them use it twice, help them generalize something a little bit neat, if you have time.

I have some other really neat crossing a room puzzles. Maybe I will put one up soon. Anyone else have favorites?

4. *Puzzle 5 25 243 1024*. Hm. These are all powers of a single prime, they are ascending, but I don’t see the sequence. Any help out there?

5. *jbl problems*? What’s jbl?

To make 24, how about 5*6 + 1 – 7?

In a previous post on searches (https://jd2718.wordpress.com/2006/08/19/and-your-question-is/), you said the question was to combine 1, 5, 6, 7 to make 21. The answer is given by a/(b – c/d), for a suitable choice of a, b, c, and d!

For puzzle 4, we have 5 = 5^1, 25 = 5^2, 243 = 3^5, 1024 = 4^5, so maybe the next number is 5^5 = 3125? That seems a little tenuous, but sometimes sequence puzzles are like that!

A nice factor puzzle is to calculate the sum of the factors of various numbers of the form 4n + 3. Then ask: why is the sum always divisible by 4?

oops. almost too easy. it is a persistent search, though less so than 3,3,8,8. maybe they want us to make a different number?

tenuous, but better than anything I noticed.

nice

JBL is me — more likely, though, people searching for that question were looking for information on what to do with their broken speaker systems (www.jbl.com).

I knew it looked like initials! I went peeking to see if Cardinal Law’s first name had been John. (I knew Bernard was in there somewhere.) But no.