Escape From The Pit
The frog was really hungry after escaping from the well, so he went to find food. He sees food inside a pit, he decided not to take it but he slipped and fell into the pit.
The pit is 54 meters high, and the frog fell into the bottom of it. At the bottom he found food that weighs 300g. He decided to bring the food with him as he starts to climb out of the pit.
His normal jump length is 600cm per day. But with the food he is carrying, he could only jump his normal length minus the weigh of the food. At night he would slip the weigh of the food in centimeters.
He eats 50g of the food at the end of every day before nighttime. So if he had 300g when he started jumping at daytime he would only have 250g before nighttime. When he has no food left he would jump his normal length and not slip at night.
(If he has 300g of food then his jump length per day will be 600-300=300cm. Then at night he would slip 250cm because he ate 50g of the food in before nighttime. This will go on and on until he has no food left. )
How many days would it take the frog to escape from the pit?
The answer is 12.
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1 solution
Pit Height=5400cm
First Day: 600cm-300g=300cm
First Night: 300cm-(300g-50g)=50cm
Second Day: 50cm+(600cm-250g)=400cm
Second Night: 400cm-(250g-50g)=200cm
Third Day: 200cm+(600cm-200g)=600cm
Third Night: 600cm-(200g-50g)=450cm
Fourth Day: 450cm+(600cm-150g)=900cm
Fourth Night: 900cm-(150g-50g)=800cm
Fifth Day: 800cm+(600cm-100g)=1300cm
Fifth Night: 1300cm-(100g-50g)=1250cm
Sixth Day: 1250cm+(600cm-50g)=1800cm
Sixth Night: 1800-(50g-50g)=1800cm
The frog has finish all the food.
Seventh Day: 1800cm+600cm=2400cm
Eighth Day: 2400cm+600cm=3000cm
Ninth Day: 3000cm+600cm=3600cm
Tenth Day: 3600cm+600cm=4200cm
Eleventh Day: 4200cm+600cm=4800cm
Twelfth Day: 4800cm+600cm=5400cm
So it takes 12 days and a lot of working out.