FILE No.58Unsolved
A note was stuck to the door of a safe.
2, 6, 12, 20, 30, □
The note ends with: "The number in □ is the first two digits of the code."
There is one rule in the row of numbers.
What number goes in □?
If you get stuck, open the hints one at a time, in order.
Work out the differences between neighboring numbers.
The row of differences also has a rule.
What if you write each number as a product?
What number goes in □?
Choose the answer closest to the truth.
42
The answer is 42.
Look at the differences: 6 - 2 = 4, 12 - 6 = 6, 20 - 12 = 8, 30 - 20 = 10. The differences increase by 2: 4, 6, 8, 10. The next difference is 12, so 30 + 12 = 42.
There is another way to see it: 2 = 1 x 2, 6 = 2 x 3, 12 = 3 x 4, 20 = 4 x 5, 30 = 5 x 6. The next is 6 x 7 = 42.
You look only at how the numbers grow and answer by hunch without searching for the rule.
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