Number Problem

[Dee-M-See]

What number, when added to a number Ten times bigger gives a number which,
When its first digit is multiplied by Four and again added to the result = 1000

[ageing fast]

If I have understood the question properly, I think it is 88.

88 + 880 = 968
8 x 4 = 32

968 + 32 = 1000

[sarumite]

Looks good to me ageing fast!

[Dee-M-See]

Thank you very much ageing fast a very prompt reply
Although I think it is my brain that is ageing fast

[Russ Bee]

The second bit of the puzzle relates to the value of 4a, for any number with the integers ab, which clearly must be less than or equal to 36 (since a can't be any bigger than 9). Consequently, the number x (which =ab), must be greater than or equal to 88, since x + 10x has to be greater than or equal to 964, i.e. 11x must be greater than or equal to 964 (i.e. 1000-36).

So, we can test the value of the integer a simply by knowing that it can only be 8 or 9; simply looking at a=9, we can readily see that 4a=36, but we know that the value of 11x would be >990, as ab>90. This means that the integer a must be 8. Now we only have two choices of b=8 or 9; testing again shows that x=ab=88, since we know that for x=89, then 11x would be 979 and would not equal 1000-4a.

We can prove this by calculating 11x=968 and 4a=32, i.e. we meet the conditions required.