You may also like

problem icon

Domino Square

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

problem icon

4 Dom

Use these four dominoes to make a square that has the same number of dots on each side.

problem icon

Sandwiches

Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's there is one digit, between the two 2's there are two digits, and between the two 3's there are three digits.

Day of the Triffids

Stage: 4 Short Challenge Level: Challenge Level:1
Let the number of ivy, nightshade and triffid plants be $i$, $n$ and $t$ respectively.

Then:

$2i + 9n + 12t = 120$ and $i + n+ t = 20$, where $i> 0$; $n> 0$; $t> 0$.

Multiplying the second equation by $2$ and subtracting the new equation from the first:
$$7n + 10t=80$$
Thus $$7n = 10(8-t)$$
Therefore $n$ is a multiple of $10$ and since $1 \le n < 20$, $n=10$

Hence $8-t=7$ and therefore $t=1$.

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