 Friday, March 23, 2012

A few weeks ago a number challenge arrived via Facebook.
It said that the following problem can be solved by pre-school children in 5-10 minutes, by programmers - in 1 hour, by people with higher education... well, check it yourself!
8809=6
7111=0
2172=0
6666=4
1111=0
3213=0
7662=2
9313=1
0000=4
2222=0
3333=0
5555=0
8193=3
8096=5
7777=0
9999=4
7756=1
6855=3
9881=5
5531=0
2581=?

I thought and thought and thought and couldn't figure it out.  Pre-schoolers! It must be something not related to any kind of computation. Numbers, shapes, squiggles...  After a while I cheated and  found the solution on the web.

It is the number of loops in the digits.
2581 will have only 2 loops in the digit 8, so 2581=2

To boost self-confidence of those who like me couldn't solve this pre-schooler challenge I am offering another one that uses a bit more math wisdom:

What is the next number in the following sequence:
-2, 4, -12, 48, -240, ?

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

Kim said...

The first number is -2, we get to the next number by multiplying by -2, then by -3 then by -4 and then by -5. So to get to the next number, we multiply by -6:

-240*-6= 1440

Jen said...

1440

V said...

1440

V said...

1440

Dennis (Of Dennis and Katrina) said...

The next number in the sequence is 1440.

4 = -2 * -2
-12 = 4 * -3
48 = -12 * -4
-240 = 48 * -5

-240 * -6 = 1440.

Dennis (of Dennis and Katrina)

Ellina said...

-1440

Ellina said...

Wait no, it's 1440, not -1440

The sequence is: -2*-2=4, 4*-3=-12, -12*-4=48, 48*-5=-240, -240*-6=1440

James said...

It's 1440.

2 x 2= 4
4 x 3= 12
12 x 4=48
48 x 5= 240
240 x 6 = 1440. Sign switches between alternate numbers in the sequence.

Jerome said...

answer_0 = -2 Start of loop
answer_1 * - 2 =-2*-2 = 4
answer_2 * - 3 = 4*-3 = -12
answer_3 * -4 = -12*-4 = 48
answer_4 * -5 = 48*-5 = -240
answer_5 * -6 = -240*-6 = 1440
::
::
::
where n is the entry number.

Ilya said...

I am glad I am not solving the "loops" puzzle, that one would have brought me to my wits' end.

The answer to the second sequence puzzle is 1440. To get each successive number in the sequence, you multiply its predecessor by -N, where N is the position index of the number in the sequence you are trying to determine. In fact, what we get is the factorial function with changing sign, multiplied by 2 (since we started with -2).

Anonymous said...

1440

Tom said...

My guess is 1200

multiply by -2, -3, -4, -5 etc

Wang said...

Looks like you are multiplying by -2, -3, -4...

4 / -2 = -2

-12 / 4 = -3

48 / -12 = -4

-240 / 48 = -5

Therefore, the next number in the sequence is -240 * -6 = 1440

TMS math said...

My class says it is 1440 because:
-2 * -2 = 4
4 * -3 = -12
-12 * -4 = 48
48 * -5 = -240
-240 * -6 = 1440

Annie said...

1440

Each number is multiplied by increasing negative numbers. -2 x -2 = 4 x -3 = -12 x -4 = 48 x -5 = -240 x -6 = 1440

Lance Hoopes said...

The next number is 1440 (-240 x -6)

Lance Hoopes said...

The next number is 1440 (-240 x -6)

SteveGoodman18 said...

This is SteveGoodman18. It appears that each term is being multiplied by the next negative integer in order to get each successive term.

If we just multiplied 48 by -5 to get -240, now we multiply that by -6 to get 1440.

Or, we develop the formula a(n) = 2*(n)!*(-1)^n.

We need the sixth term, so a(6)=1440.

Anonymous said...

every number is one greater than the former multiplier. 5 is the multiplier of 48 to get -240 but every other multiplier is a negative number so -6 times -240 equals 1440.

Gurubandhu m,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

To get from the first number in the sequence to the second, multiply by -2. To get from the second to the third, multiply by -3, then -4 and so on. The next number in the sequence is -240 x -6 = 1440.

Jerome's wife said...

The answer of the suceeding numbers -2, 4, -12, 48, -240 is 1440.

Donna said...

The pattern is x(-2), then x(-3),then x(-4) etc, so the next number would be -240 x (-6) = 1440.

Anonymous said...

1440?

The negative and positive signs are alternating. Just take all the - signs out. 2x2=4 4x3=12 etc. So, just multiply the first number by 2, multiply the number you get by 3, etc. My explanation might be lousy as I am just 13.

Anonymous said...
This comment has been removed by a blog administrator.
TracyZ said...

I think the next number in the sequence is 1,440.

2 x 2 = 4
4 x 3 = 12
12 x 4 = 48
48 x 5 = 240
240 x 6 = 1,440

At first I was considering complicated equations involving powers of 2 to find this solution. Thanks go to my spouse for helping me see it wasn't as complicated as that.

anne-marie said...

Hi,
I will say -12 *(-240)*100= 288000

Rojan Galvez said...

1440

Anonymous said...

My answer is: 1440

-2, 4, -12, 48, -240
Here's the pattern I see that yields 1440:

1. The multiplier in sequence is 2,3,4,5
Thus, 6x240=1440
And you alternate the sign

Barry Gerard

Anonymous said...

Sharron Fortier via email:
The answer to the current question is 1440.

Maria said...

Wow! So many answers.
It is 1440 and everyone who wrote it gets a puzzle point. Now, I will need a separate blog just to keep the scores :)
See you next week.

Maria said...

By the way, those who submitted as anonymous, please feel free to type your name in the comments below to get a puzzle point.

Anonymous said...

1440

jessica said...

I'm guessing 1440!

Anonymous said...

It's 2 :) for sure