Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

14 Divisors

What is the smallest number with exactly 14 divisors?

Summing Consecutive Numbers

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Different Digital Clock

Stage: 3 Short Challenge Level:
All six digits are different $360$ times between $10$:$00$:$00$ and $11$:$00$:$00$.

To satisfy the stated condition, the display will have the form $10$:$m_{1}m_{2}$:$s_{1}s_{2}$.

The values of both $m_{1}$ and $s_{1}$ have to be chosen from $2$, $3$, $4$, $5$. So there are four ways of choosing $m_{1}$ and three choices for $s_{1}$. Since four digits have been chose, $m_{2}$ and $s_{2}$ are selected from the remaining six.

Thus the total number of times is $4 \times 3 \times 6 \times 5 = 360$.

This problem is taken from the UKMT Mathematical Challenges.

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