You may also like

problem icon

Consecutive Numbers

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

problem icon

14 Divisors

What is the smallest number with exactly 14 divisors?

problem icon

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?

Double with 1-9

Stage: 3 Short Challenge Level: Challenge Level:1

The answer can be any one of:
$(6729,13458)$, $(6792,13584)$ , $(6927,13854)$, $(7269,14538)$,
$(7293,14586)$ , $(7329,14658)$ , $(7692,15384)$ , $(7923,15846)$,
$(7932,15864)$ , $(9267,18534)$ , $(9273,18546)$ , $(9327,18654)$  
To try and reach one of these, you know that the first of the digits in the answer must be a $1$ that is carried. Any odd digit in the answer means the digit before in the original number must have been at least $5$.

Since we know where the $1$ must go, if $5$ was not in the answer, the number beneath it would either be $0$ or $1$, depending on whether there was a carry, but there is no $0$ and the $1$ has already been used.

After this you need to work systematically until you can find a solution.

This problem is taken from the UKMT Mathematical Challenges.
View the archive of all weekly problems grouped by curriculum topic

View the previous week's solution
View the current weekly problem