Garden And Gossip Forums

{1,2,3} ?

Following on from this puzzle, is one from another book.

6 is a Perfect Number because the 3 numbers that divide it exactly, add up to the number 6.
There are only 2 more Perfect numbers below 500.
Can you find them?

I know both but here's just one 496

Both Martin and the Boss are so good at these number puzzles. Do you both already know the answers or do you work them out. I'm left way behind.

I knew because I helped my grandson (11) with his homework

I haven't done this one. I tried a few potential candidates but nothing worked out. I can't think of a way of finding the answer other than just trial and error, so lost interest quickly

(14-11-2021, 02:57 PM)MartinH Wrote: [ -> ]I haven't done this one. I tried a few potential candidates but nothing worked out. I can't think of a way of finding the answer other than just trial and error, so lost interest quickly

28 = 14 + 7 + 4 + 2 + 1

I've no idea how to find the answer either but 28 & 496 are the correct answers.

I can't ask you all the puzzles as some need diagrams that I can't replicate. Next question is another numbers one, sorry.

Take the number 80 and divide it into four parts - four numbers which add up to 80, so that :-

If you add 3 to the first number
Subtract 3 from the second number
Multiply the third number by 3
and divide the fourth number by 3
You will be left with the same answer.

What are the original four numbers that make up 80?

Oooh, algebra practice!
12, 18, 5, 45.
That was fun!

a+3 = b-3 = c*3 = d/3
a+b+c+d = 80
a+a+6+(a+3)/3+(a+3)*3 = 80
a+a+6+a/3+1+3a+9=80
5a+a/3=64
16a=192
a=12
b=18
c=5
d=45

That was clever Martin, my long forgotten algebra vaguely understood all the steps. Thanks for showing the workings.
Are numbers your trade. they're certainly not mine!