Brain Teasers
Waldo's Peanuts
Waldo ate a total of 100 peanuts in 5 days. Each day, he ate 6 more peanuts than he did the day before. So, how many peanuts did Waldo start with on the first day?
Hint
Example; if Waldo started with 20 peanuts on day 1, he should have eaten 26 peanuts on day 2. By then, he would have eaten a total of 46 peanuts in 2 days. 20 is not the correct answer though, because by day 5, he would have eaten 160 peanuts.Answer
Waldo ate 8 peanuts on day 1. He had 14 peanuts on day 2 and added 6 peanuts each day up to day 5. By day 5, Waldo would have eaten a total of 100 peanuts.Hide Hint Show Hint Hide Answer Show Answer
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Ha! say I, who knows way too many shortcuts to these.
Let x be the number of peanuts eaten in day one.
100=(x)+(x+6)+(x+12)+(x+1+(x+24)
100=5x + 60
100 - 60 = 5x
40/5 = 5x/5
8=x
there he ate 8 peanuts on day one.
if there is a shorter way to solve this llet me know...hehehehe
100=(x)+(x+6)+(x+12)+(x+1+(x+24)
100=5x + 60
100 - 60 = 5x
40/5 = 5x/5
8=x
there he ate 8 peanuts on day one.
if there is a shorter way to solve this llet me know...hehehehe
Right, it's easy actually, if you think a bit.
easy
very easy!
very easy!
If Waldo ate X peanuts in D days and ate P more peanuts each day than he did the day before, then the number of peanuts Waldo ate on the first day is:
W = (X - P * ((D - 1)^2 + D - 1) / 2) / D
W = (100 - 6 * ((5 - 1)^2 + 5 - 1) / 2) / 5
W = (100 - 6 * (4^2 + 4) / 2) / 5
W = (100 - 6 * 20/2) / 5
W = (100 - 6*10) / 5
W = (100 - 60) / 5
W = 40 / 5
W = 8
I'll leave it to the reader to figure out how to derive the formula.
W = (X - P * ((D - 1)^2 + D - 1) / 2) / D
W = (100 - 6 * ((5 - 1)^2 + 5 - 1) / 2) / 5
W = (100 - 6 * (4^2 + 4) / 2) / 5
W = (100 - 6 * 20/2) / 5
W = (100 - 6*10) / 5
W = (100 - 60) / 5
W = 40 / 5
W = 8
I'll leave it to the reader to figure out how to derive the formula.
Actually, I forgot one reduction in the formula, so while the formula above is correct, it can be expressed more compactly as:
W = (X - P * (D^2 - D) / 2) / D
W = (100 - 6 * (5^2 - 5) / 2) / 5
W = (100 - 6 * 20/2) / 5
W = (100 - 60) / 5
W = 40 /5
W = 8
W = (X - P * (D^2 - D) / 2) / D
W = (100 - 6 * (5^2 - 5) / 2) / 5
W = (100 - 6 * 20/2) / 5
W = (100 - 60) / 5
W = 40 /5
W = 8
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