Sample Puzzle
Minimize the sum
Grade 5–6
Number manipulation
Place value
Partitioning
The number 6123578 is written on a sheet. You cut the sheet twice, obtaining 3 numbers by keeping the order of digits. What is the smallest possible sum of these three numbers?
Hint 1
Place two cuts between digits, e.g. 6 | 123 | 578. Each part becomes a separate number and you add them. Slide a cut left or right and notice how moving it left can shrink place value (hundreds → tens → ones) for many digits in the right group.
Hint 2
Compare these three possible cuts (don’t sum yet — estimate, then compute):
6 | 123 | 57861 | 235 | 78612 | 35 | 78
Which total is the smallest?
Show solution
Group digits to keep early numbers small and avoid large place values. The best among the examples is 61 | 235 | 78 with 61 + 235 + 78 = 374. It’s also minimal among all two‑cut partitions for 6123578.