When Mr Johnson was over 50 but less than 80 he told a friend: "Each of my sons has as many sons as brothers, and the number of my years is exactly that of the number of both my sons and grandsons." How many sons and grandsons had
Mr Johnson?

Question

When Mr Johnson was over 50 but less than 80 he told a friend: "Each of my sons has as many sons as brothers, and the number of my years is  exactly that of the number of both my sons and  grandsons." How many sons and grandsons had
Mr Johnson?

anonymous · Answer

is this harder than i think? or am i making a mistake?

anonymous · Answer

I think it's pretty hard :D

anonymous · Answer

i am thinking you can guess and check for this one

anonymous · Answer

say five sons
then each son has 4 children
so there are 5 sons and 20 grandsons for a total of 25
ok that doesn't work, try a bigger number

anonymous · Answer

Bingo! Eight sons and 56 grandsons. So he was 64, right?

anonymous · Answer

$$8\times 7+8=8^2=64$$ yup

anonymous · Answer

if you want to sound fancy you can say that 64 is the only perfect square between 50 and 80 since $7^2=49$ and $9^2=81$

anonymous · Answer

Thank you :)