To be divisible by 4, last 2 digits must be div by 4. So y can be 0, 2, 4, 6 or 8.

Now to be divisible by 11, |(the sum of the digits in even places) – (the sum of the digits in odd places)| should be divisible by 11 (or should be 0)

Sum in odd places is 18 + x and in odd is 13 + y, trying out the various values of y we find that when y = 0, x = 6 to satisfy the condition, similarly
when y = 2 x = 8,
when y = 4, no value of x exists
when y = 6, x = 1 and
when y = 8, x = 3.

If you know the logic, you can generate it in 20-30 seconds anyway. And if you use it a lot then chances are the first 5-6 lines at least may stay in your memory without consciously trying to memorise (I know till line 8 though I never actually sat down to mug it up, just use these numbers so often…)

Yes, I figured it isn’t that difficult if one uses it often. Thanks a lot. ðŸ™‚

I am sure people must have mentioned this to you, but nonetheless hearing it again wouldn’t hurt :p.
J, what you are doing here via these posts is pretty legendary. You are a blessing. ðŸ™‚
Students like me are indebted to you for life. Thank you very much, again.

This is cool !

Off topic: What is the least value of x if the nine digit number 23x4567y4 is divisible by 44 ?

Your help would be really beneficial. Thank you.

23x4567y4 is divisible by 44 i.e. 11 and 4.

To be divisible by 4, last 2 digits must be div by 4. So y can be 0, 2, 4, 6 or 8.

Now to be divisible by 11, |(the sum of the digits in even places) – (the sum of the digits in odd places)| should be divisible by 11 (or should be 0)

Sum in odd places is 18 + x and in odd is 13 + y, trying out the various values of y we find that when y = 0, x = 6 to satisfy the condition, similarly

when y = 2 x = 8,

when y = 4, no value of x exists

when y = 6, x = 1 and

when y = 8, x = 3.

So minimum x is 1 I guess.

regards

J

Thanks a lot. You guys rock !

May trouble you more though ðŸ™‚

Please do ðŸ™‚ We will help if we can!

J

Hi J, would you advise that we memorize Pascal’s Triangle, or just knowing the logic of it sufficient?

If you know the logic, you can generate it in 20-30 seconds anyway. And if you use it a lot then chances are the first 5-6 lines at least may stay in your memory without consciously trying to memorise (I know till line 8 though I never actually sat down to mug it up, just use these numbers so often…)

regards

J

Yes, I figured it isn’t that difficult if one uses it often. Thanks a lot. ðŸ™‚

I am sure people must have mentioned this to you, but nonetheless hearing it again wouldn’t hurt :p.

J, what you are doing here via these posts is pretty legendary. You are a blessing. ðŸ™‚

Students like me are indebted to you for life. Thank you very much, again.