### Brain Teasers

# Melvin the Wizard

Melvin the Wizard has some magic blue orbs.

Every day 1 disappears.

Every 2 days 1 goes green.

Every 4 days 1 green orb disappears instead of another blue one.

From these facts, determine what the ratio of blue to green (or vice versa) orbs remaining is from the beginning to the end of February in the Year 2292. He has 50 orbs at the start of February.

Every day 1 disappears.

Every 2 days 1 goes green.

Every 4 days 1 green orb disappears instead of another blue one.

From these facts, determine what the ratio of blue to green (or vice versa) orbs remaining is from the beginning to the end of February in the Year 2292. He has 50 orbs at the start of February.

### Hint

It is easier to work it out in a 10 x 5 grid.### Answer

The ratio is 1 : 2 (green : blue).If you draw a 10 x 5 grid, cross out a square for each orb that disappears. Put a circle in each box for each green orb. The year 2292 is a leap year, so there are 29 days in the month (February). Mark each 'day' you work out. You will find on each row, you get 4 disappeared orbs and 1 green orb. This pattern continues, so when you have counted 29 days, there are 14 blue orbs remaining and 7 green ones. This gives you the ratio of 1 : 2 (green : blue)

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