🔢 Gauss Trick 📚 Grade 4 ⏱ 6 min
The Gauss Trick: Adding 1 to 100 Fast
Legend says young Gauss solved this in seconds while his teacher expected it to take an hour. Here is his trick.
Pairing sums
1+100=101, 2+99=101, 3+98=101 — every pair from the ends gives the same sum, 101. There are 50 such pairs total.
💡 Anchor: write numbers 1 to 10 in a row, and below them 10 to 1 in reverse — each column gives the same sum.
The Gauss formula
Fast calculation: 50 pairs × 101 = 5050 — the whole sum from 1 to 100 in a couple of steps instead of a hundred additions.
FAQ
Does the trick work for other ranges?
Yes, the same principle works for the sum from 1 to any number — just the paired numbers change.