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# Punky Fish

##### Age 14 to 16 ShortChallenge Level

Starting with females
Every fish has at least 8 stripes
10 fish with 8 stripes have 80 stripes
There are 6 more stripes
As a male fish has one extra stripe, these 6 stripes must belong to 6 male fish.

So there are 6 males and 4 females.

Therefore the ratio of male to female fish is 3:2.

Starting with males
Now $86=9\times9 + 5$
$=9\times 8+9+5 = 9\times8+14$
$=9\times 7+18+5 = 9\times7+23$
$=9\times 6+27+5 = 9\times6+32=9\times6+8\times 4$

Therefore the ratio of male to female fish is $3:2$.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.