Henry Ernest Dudeney/Puzzles and Curious Problems/170 - The Six Noughts

Puzzles and Curious Problems by Henry Ernest Dudeney: $170$

The Six Noughts

    A     B     C
  111   111   100
  333   333   000
  555   500   005
  777   077   007
  999   090   999
 ----  ----  ----
 2775  1111  1111
 ----  ----  ----

Write down the little addition sum $A$, which adds up to $2775$.

Now substitute $6$ noughts for $6$ of the figures, so that the total sum shall be $1111$.

It will be seen that in the case $B$ five noughts have been susbtituted, and in the case $C$ nine noughts.

But the puzzle is to do it with six noughts.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $170$. -- The Six Noughts
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $235$. The Six Zeros