3-round logic challenge

Ilustração de um balão com ponto de interrogação e quadros com círculo, triângulo, quadrado e interrogação

✓ Question 3: 17

Round 1 of 3 · Question 4 of 520% complete

What number comes next?

1491625?
30
34
36
49

Why, in question 3: What number comes next?

The answer is 17. The differences between the numbers grow by 1 to 1: plus 1, plus 2, plus 3, plus 4. The next difference is more 5, and 12 + 5 = 17.

When the difference also follows a pattern

Not every sequence always grows by the same amount. Sometimes the rule is hidden in the differences: write them on a second line, below the numbers, and look for the pattern in them.

In this question, the second line is 1, 2, 3, 4. It's a simple sequence, and its next step, 5, tells you what to add to the last number.

If the second line still doesn't show a clear pattern, you can repeat the trick and calculate the differences of the differences. The difference engine, designed by Charles Babbage in the 19th century, was intended precisely to compute tables using this method.

A common trap is to look only at the last two numbers. The correct rule has to work for the entire sequence, from the first to the last term.

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