# Learning with numbers under connectivism?

I found this from Daniel’s blog:

 Finish this sequence of equalities… Posted: 10 Jan 2009 05:00 PM CST 8809 = 6 7111 = 0 2172 = 0 6666 = 4 1111 = 0 3213 = 0 7662 = 2 9312 = 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 = ? Hint: See Daniel’s blog Source: Misha Lemeshko Postscript:  Answer: See Comment no. 9 in Daniel’s blog left by me, and it seems I got the answer but from a “different logic “(to acknowledge Daniel and Misha in posting this mathematical problem)  (Comment No. 11 provides the answer with full explanation) 2581 = 2 map 0, 6, and 9 to a value of ‘1′ map 8 to a value of ‘2′. map any other digit to ‘0′ sum up mapped digit values of the left number and you obtain the number on the right. examples: 8809 = 6: 8(2) + 8(2) + 0(1) + 9(1) = 6 2222 = 0: 2(0) + 2(0) + 2(0) + 2(0) = 0 6855 = 3: 6(1) + 8(2) + 5(0) + 5(0) = 0 therefore, 2581 = 2: 2(0) + 5(0) + 8(2) + 1(0) = 2 Comment by David — 11/1/2009 @ 20:31 Many thanks to Daniel and Misha Lemeshko for your stimulating problem.  And David for the answer.

How important is patterning in learning?

What could be learnt from such problem?

Do you have any such problems available to challenge other learners and educators?

Do these problems attract your attention in learning or blogging?

Do you use these challenges to motivate other learners or educators?

## 14 thoughts on “Learning with numbers under connectivism?”

1. This very problem is absolutely useless. But one can make fun of it!

2. suifaijohnmak says:

I learnt that by comparing numbers, you could still get the “correct” answer by “analysis”, though the logic behind could be wrong. In the same way, when I am reviewing information from blogs, I could make the “same judgment” based on my perception of the data presented, though my interpretation may be incorrect.
This teaches me to see things differently, as I could be right (in answer), but wrong (in logical reasoning). But at the end, if it opens up more learning for me, then it’s good, and I could reflect on its implication….
John

3. I like your solution. Somewhat more satisfying than just “count the loops.”

4. Rafał says:

I knew that riddle as a problem for preelementary school kids. I was trying to focus how to solve this with a knowledge available for six year old. The can’t even add numbers properly (usually).
And I gave it to a kid and then… eureka!
He got bored and filled closed spaces of the numbers.
Like “8” got two “tummys” and “9” got only one.
This is crazy :D

5. Franc says:

i had to admit that solving this kind of problem with the knowledge i learn from school is almost time consuming.We do think too complicated,but when solve it the other way round,i discover ” Hey,why should we all think it so complicated”.Thank for sharing this ~

6. Sorry to say that but this puzzle is absolutely useless for most purposes.

This is not a “pattern” arising from intrinsic properties of numbers or even base-dependent properties, as you would have obtained if it was designed as a computation of arithmetic residues. This is just an arbitrary coding with elicits only a kind of guessing. This makes most proposed solution rules for this problem akin to numerology/arithmomancy. Precisely people magazines have numerology columns where you get a prediction according to your “number” constructed as a sum of the values attributed to letters of your name…

Fighting against a feeling of arbitrariness and exclusion in mathematics is one of the most important implicit goals of mathematical teachers. Each time you use numbers in front of your student for something else than their intrinsic properties you take a very strong risk. When I interview young students (from age 6 to 16 mostly), the older they are, the larger the proportion answering a question about “why is [basic mathematical fact in their class or the year before] true ?” by “Because the teacher says so.” Which is a very good predictor of dropping math and science as subjects in subsequent years.

I would give this kind of problem only as an amusement, a puzzle, certainly not presenting it as mathematics, but cryptography and only to students already good autonomous problem solvers, and then reviewing with them their solving strategy and their opinion of the interest (not the difficulty because it is irrelevant — you can make such puzzle as complicated as you care to do) of the problem.

7. Yes, it could be a puzzle. How about using this as analogy in why we don’t understand the rules that were made up by others, probably due to a different algorithms set up which is different from the usual ones, and we were asked to crack the riddle? If the students understand the rules behind this sort of puzzle, would they see things differently when confronted with more complicated problems? At least, this would arouse their curiosity in thinking it through……
Thanks for your sharing of its uselessness.

8. szdoc says:

I think ogerard should take it easy. I think it is a fun problem. This kind of problem makes one use and stimulate the nondominant parietal lobe. Trust me, I am a neurologist:)

9. Bayya says:

Don’t think far with this. The logic lies in the number of ‘holes’ in the numbers. 0,4,6,9 = 1 (hole) 8=2 (holes) all other numbers have no ‘holes’ so they’re 0.

10. amira.G says:

Bayya’s logic makes the most sense. pre-schoolers would know shapes or ‘holes’ as opposed to mapping numbers to other numbers.

11. irish joy PHD says:

i found it only for about 2 minutes… it counts how many cirlcles are in the numbers..OMG.. so easy

12. Bayya – except that 4 could either be a 1 or a 0, depending on the font or your handwriting. Which is why none of the sequences of numbers include it!