Rethinking Counting

Logic Level 1

Ok, forget everything your teachers taught you about how to count. Now, which of the following numbers has the lowest value if:

1 > 2 3 < 4 6 > 7 2 > 5 7 > 3 5 > 4 \begin{aligned} 1&>&2 \\ 3&<&4 \\ 6&>&7 \\ 2&>&5 \\ 7&>&3 \\ 5&>&4 \end{aligned}

To clarify: " > > " and " < < " denote the greater than symbol and less than symbol respectively.

7 3 5 2

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Trevor Arashiro by Trevor Arashiro , 22, USA

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8 solutions

Victor Loh
Jul 1, 2014

We have 1 > 2 > 5 > 4 > 3 1>2>5>4>3 and also 6 > 7 > 3 6>7>3 so the desired answer is 3 \boxed{3} .

54 Helpful 0 Interesting 0 Brilliant 0 Confused

1>2>5>4>3<7<6 here the least is 3

nikhil reddy - 6 years, 7 months ago

absolutely agree ^^ really really easy

Huynh Julie - 5 years, 11 months ago

That's exactly how I solved it.

Andy Freund - 5 years, 12 months ago

I got it wrong when I read 'forget how to count'... so I picked 7 (there wasn't a seventh option :-P)

Eric Hammer - 6 years, 3 months ago
Vaibhav Singh
Jun 26, 2014

Any number, on the left side of the greater than sign cannot be the smallest.

so, 5,2,7 are struck off and we are left with 3 only.

25 Helpful 0 Interesting 0 Brilliant 0 Confused

If we study it, the proper ascending order is- 3-7-6-4-5-2-1

5 Helpful 0 Interesting 0 Brilliant 0 Confused

This is correct if you assume that 6 < 4. You could well assume that 4 < 7 < 6 < 5 and then the ascending order would be 3-4-7-6-5-2-1. What I am saying is that you don't have any information about the ascending order unless if you see a pattern behind these numbers that I don't.

Kyriakos Sideris - 6 years, 10 months ago
Biqar Boy
Jul 26, 2015

Create a directed graph where edge x -> y means that x is less than y. Now apply topological sorting and you will get the answer.

In this problem, the edges will be like this: 2->1, 3->4, 7->6, 5->2, 3->7, 4->5. After drawing this you will get 3 as the root and no other number is less than this.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Would be great to illustrate that with a picture.

Tony Flury - 5 years, 9 months ago

3,4,5,2,1,7,6 That's the ascending order I found that satisfied all the information. Therefore, the answer is 3.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
William Hsu
Jul 7, 2015

To get rid of any bias of previous knowledge of numbers, we can map each number to a letter (because why not?) let 1 be A, 2 be B, 3 be C, 4 be D, 5 be E, 6 be F, and 7 be G. Rewriting the problem: A > B C < D so D > C F > G B > E G > C E > D

Then: A > B > E > D > C and G > C, too and F > G, so F > G > C, therefore C must be the least, and that's 3 in this case.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

you made that way more complicated than it needed to be lol

Kate McFadden - 5 years, 4 months ago

I did the same

Prathamesh Kulkarni - 5 years, 4 months ago

Swear that 2 is the answer cuz 4 is bigger then 3, 5 is bigger then 4 and then 2 is bigger then 5 so got to be 2

Thomas Doherty - 5 years, 5 months ago

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2 is bigger than 5, so 2 can't be the smallest.

Steve Scott - 5 years, 4 months ago
Neo Ko
May 11, 2017

Easiest method is the process of elimination. You have numbers 1 to 6. Just eliminate the numbers which are on the greater end of each logic statement. For example, eliminate 1, 4, 6, 2, 7, and 5. You're left with 3.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Jimmy Schwing
Feb 17, 2016

The order could be 3 4 5 2 1 7 6

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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