Spy

Where addition and multiplication call it a tie.

A number whose digit sum equals its digit product, like 123 (1+2+3=6=1×2×3) or 22 (2+2=4=2×2). Sum and product — the two most basic operations — ending in a draw.

98
Exact matches
1 in 10,204
Odds
0.0098%
Share
266 EP
Base EP

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Spy numbers are among the rarest entries in this whole category: just 98 in the entire range, 1 in 10,204. The reason is hard math — the digit product grows exponentially with length while the digit sum grows at most linearly (9 per digit). For the two to meet, multiplication has to show extreme restraint.

First iron rule: any zero disqualifies you (the product collapses to 0 while the sum stays positive). Second rule: 1 is the only tuner — it raises the sum without touching the product, so nearly every multi-digit Spy is padded with 1s, like 1124, 1412, and the range champion 621111 (6+2+1+1+1=11=6×2×1×1×1).

All single digits 1–9 qualify automatically (sum and product are both itself); the real intrigue is multi-digit. Of the 98 seats, 9 go to single digits, leaving 89 one-in-a-million coincidences — roll a six-digit Spy and take a screenshot.

Smallest examples

Notable examples

123 The Spy calling card: 1+2+3 = 1×2×3 = 6 — and a straight 1-2-3 to boot.
621,111 Largest Spy in range: a 6, a 2 and four 1s — sum and product both 11.
22 2+2=2×2=4. Also a palindrome with matching ends — a tiny overachiever.

Related Entries

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