September 21, 2024

Math Puzzle: What Number is Missing?

A grid shows the following numbers and characters in four rows: first row: 11, 23, 1214, 41, 59; second row: 13, 29, 1316, 43, 61; third row: 17, 31, 1422, 47, 67; fourth row: 19, 37, ?, 53, 71. — Hans-Karl Eder/Spektrum der Wissenschaft, restyled by Amanda Montañez

Which number should replace the question mark?

The missing number is 1,620.

The digits in the tens places (green in the figure below) of the numbers in columns 1, 2, 4 and 5 are added together. The total value is represented by the digits in the thousands and hundreds places of the number in column 3.

The digits in the ones places (black) in columns 1, 2, 4 and 5 are added together. The total value is represented by the digits in the tens and ones places of the number in column 3.

A grid highlights that for each of the rows of numbers listed above, the sum of the tens digits of the numbers in the first, second, fourth and fifth columns equals the first two digits of the number in the third column. Meanwhile adding the ones digits of the first, second, fourth and fifth columns yields the second two digits of the number in the third column. For the final row, those two calculations are 1 + 3 + 5 + 7 = 16 and 9 + 7 + 3 + 1 = 20, so the missing number is 1,620. — Hans-Karl Eder/Spektrum der Wissenschaft, restyled by Amanda Montañez

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This puzzle originally appeared in Spektrum der Wissenschaft and was reproduced with permission.