Cooking Eggs

Logic Level 1

There are two eggs timers: one for 7 minutes and one for 11 minutes. We must boil an egg for exactly 15 minutes. Can we do that only using these timers?

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6 solutions

Brian Charlesworth
Apr 30, 2016

For clock timers, (analog or digital) :

Start both timers at the same time without yet putting the egg in to the boiling water. Once the 7 minute timer expires, place the egg in the water to cook. There are then 11 - 7 = 4 minutes left until the 11 minute timer expires. After it does so, we would then immediately reset the 11 minute timer and let it run its full period. The egg would then have been in the water for 4 + 11 = 15 minutes and thus be properly cooked.

For sand timers :

Start both timers and place the egg in the boiling water simultaneously. After the 7 minute timer runs out, turn it over to start it on a new cycle. After the 11 minute timer runs out, 4 minutes of sand will have dropped to the lower portion of the 7 minute timer, so turn it over once again so that those 4 minutes of sand can run out, after which the egg will have been boiling for a total of 11 + 4 = 15 minutes as desired.

Great solution!

Paola Ramírez - 5 years, 1 month ago

this solution count as there are 3 timers.

Zulfi Robbani - 5 years, 1 month ago

It would be impossible for EXACTLY 15 minutes though, because it takes time to reset the timer, right?

§martie On Brilliant - 1 year, 3 months ago

FrEshy Pisuttisarun
May 6, 2016

Set the 7 and 11 timers together. When the 7 timer goes off, boil the egg. When the 11 timer goes off, we have had 4 minutes already so just quickly reset the 11 again for another 11 minutes. 11 + 4 = 15!

Divyapratap Chauhan
Apr 30, 2016

Before boiling the eggs start both the timmers simultaneously. When the 7 minute timmer rings, it means that there are 4 minutes left on the 11 minute timmer, and we will start boiling the eggs. When the 11 minute timmer rings which means eggs were boiling for 4 minutes and we will again start the 11 minute timmer. Thus 4 + 11 we will have 15 minutes.

Great! Can you find all the possible times you can measure using only the two given timers?

Pranshu Gaba - 5 years, 1 month ago

Maybe, using some number theory is it possible

Paola Ramírez - 5 years, 1 month ago

I think that, since $7$ and $11$ are coprime, we can measure any positive integer time interval. For example, for $1$ minute, start both timers simultaneously, restart the $7$ -minute clock after $7$ and $14$ minutes, and the $11$ -minute clock after $11$ minutes. Put the egg in the water after the $7$ -minute clock has expired at $21$ minutes and then take it out after the $11$ -minute clock has expired after $22$ minutes.

Brian Charlesworth - 5 years, 1 month ago

Puspenjit Datta
May 10, 2016

Follow below steps,
1) Start both the clock together.
2) When 7m completed one cycle, start boiling the egg. 11m still left with 4m to complete the cycle
3) Let 11m complete 2 cycles from here. First cycle will be 4m and 2nd 11m, so total 15m

Great! Thanks for explaining. I upvoted your solution (+1)

Pranshu Gaba - 5 years, 1 month ago

Mohaimen Radi
May 5, 2016

starting the both counter, when The 7 minute counter goes off, it means there are 4 minutes left in the 11 minute timer, and after it goes off, reset the 11 minute timer, and u got 4 +11 = 15 minutes precise

Thanh Nguyen
May 5, 2016

Longer way... After setting for both clock running, there will be 4 mins left in 11mins timer. I make 7mins timer to run agian with that 4 mins in the other timer, 7-4=3 mins, letting 11 mins timer run again, 11-3=8 mins, now boil the egg with 7 mins timer and 8 mins left of 11mins timer.

Cooking Eggs

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