Missing Number
🔒 Log in to trackmedium importance~1-2 Q in Tier 19 formulas⚡ 6 shortcuts3 subtopics
Every formula in this topic, grouped by subtopic. Print it and pin it above your desk.
How missing-number puzzles work
Rule check
f(a_1, b_1) = c_1 \text{ and } f(a_2, b_2) = c_2 \Rightarrow \text{use } f
One row fitting proves nothing. Two rows fitting is strong proof.
Common families
a + b,\ a - b,\ ab,\ ab \pm k,\ (a + b)k,\ a^2 \pm b
Sums and products cover most puzzles. Try them first.
Grids with row (or column) rules
Sum times a number
c = (a + b) \times k
Rows (4, 7, 22) and (6, 3, 18) give k = 2.
Square minus the second
c = a^2 - b
Rows (8, 15, 49) and (7, 10, 39) fit.
Sum of two squares
c = a^2 + b^2
Rows (3, 4, 25) and (6, 8, 100) fit.
Average of two
c = \dfrac{a + b}{2}
Rows (12, 8, 10) and (20, 6, 13) fit.
Digit-sum and digit-reversal rules
Digit sum
S(47) = 4 + 7 = 11
Add the digits of the number.
Reversal
R(43) = 34
Write the digits in the opposite order.
Digit product
P(47) = 4 \times 7 = 28
Multiply the digits of the number.