Egg Puzzler

Puzzler: The December puzzler is an extension of the November puzzler. Chris has a basket of eggs for sale. He sells half the eggs plus half an egg to Maria. Then he sold half the remaining eggs plus half an egg to Ai-Ling and finally, he sells half the remaining eggs plus half an egg to Jermaine. At the end of the three sales, Chris is out of eggs. The funny thing is that Christopher never had to break an egg. How many eggs did Chris start with? Does only one solution exist? (This is a difficult 3rd grade problem.) No eggs are hard-boiled or cut in half!

Solution: There is only one solution and the answer is 7 eggs.

In this case, Maria buys ½ of Chris's eggs + ½ of 1 egg. Ai-Ling buys ½ the eggs left + ½ of 1 egg, and Jermaine buys ½ of the remaining eggs + ½ of 1 egg. No eggs are broken and Chris has no eggs left after the three sales.

If Chris has 7 eggs for sale, Maria buys ½ of 7 eggs (3 ½ eggs) and ½ of 1 more egg. 3 ½ eggs + ½ egg = 4 eggs. Now, Ai-Ling buys ½ of the remaining eggs (7 - 4 = 3), so ½ of 3 eggs is 1 ½ eggs.

Ai-Ling also buys ½ of 1 egg for a total of 2 eggs. (1 ½ = ½ + 2)

To sum up so far, Maria has bought 4 eggs, Ai-Ling has bought 2 eggs leaving one egg for Jermaine, so 6 of 7 eggs have been sold leaving 1 egg.

Finally, Jermaine buys ½ of the remaining eggs + ½ of 1 egg. Since 1 egg remains, ½ of the remaining eggs is ½ of 1 egg. Jermaine, like all the others, also buys ½ of 1 egg. Since there is only 1 egg left, Jermaine has bought the last egg.

Egg Puzzler

Puzzler: Christopher had a basket of eggs for sale. He sold half the eggs plus one egg to Maria. Then he sold half the remaining eggs plus one egg to Ai-Ling. Finally, he sold half the remaining eggs plus one egg to Jermaine. The funny thing is that Christopher never had to break an egg. How many eggs did Christopher Start with? [What's the lowest number that Christopher could could start with?]

Solution: The answer to the November Puzzler is 14.

The key is to find an even number that, when divided by 2, has an odd answer. For example, 6 divided by 2 = 3. Then, just do the math. 14 divided by 2 = 7.

Maria buys half of Chris's eggs + 1: 7 + 1 = 8. 14 - 8 = 6 eggs remaining.

Ai-Ling buys ½ of the remaining eggs +1: 6 divided by 2 = 3: 3+ 1 = 4 eggs sold to Ai-Ling.

Jermaine buys ½ of the remaining eggs + 1: (Maria bought 8, Ai-Ling bought 4 which leaves 2 eggs.) 2 divided by 2 = 1: 1 + 1 =2, so Jermaine buys 2 eggs.

Between the three, they have bought 14 eggs.

Digit Puzzler

Puzzler: Take the number of your fingers multiplied by the number of your toes divided by one half. Then add it to the number of months in a year. What is the total?

Solution: Assuming you have all your fingers and toes and no extras, 10 fingers X 10 toes = 100. 100 divided by one half = 200. 200 + 12 months = 212.

Muffin Puzzler

Puzzler: Goldilocks's grandmother hands a basket of freshly made peanut-butter-and -chocolate muffins to Goldilocks and says, "These are for you, darling, but they just came out of the oven and need to cool before you can eat them. Please set them outside on the porch. You can enjoy them later."

Goldilocks thanks her grandmother and carefully places the basket on the front porch of their forest home. She then goes inside to take a nap while the muffins cool.

Three bears stroll by the cottage and smell the wonderful aroma of the muffins. They follow the smell right to Goldilocks's front porch and smile when the see both the nameplate on the door and the basket of muffins. Papa Bear approaches the basket first and eats exactly ¼ of the muffins.

"Mmm," groans Papa Bear, "These are yummy."

Next Mama Bear eats exactly 1/3 of the remaining muffins. "You are right Papa, "she declares. "These are yummy."

Finally Baby Bear goes to the basket and eats exactly ½ of the muffins left by Mama Bear. He licks his lips and says,"Mmm, much better than porridge."

The three bears pat their full tummies; smile contentedly at one another and continue their walk through the forest.

When Goldilocks awakens from her nap, she immediately runs to the porch to grab the basket of muffins. She is startled to discover that only 3 muffins remain in the basket. "What happened to all the muffins?" she exclaims. "I know there were more than 3 in this basket when I put it here. I wonder how many muffins were in the basket to begin with?"

Use the information in the story to help Goldilocks determine how many muffins were in the basket. If Papa Bear took ¼ of the original muffins, Mama Bear took 1/3 of what he left, Baby Bear took ½ of what remained, and only 3 muffins are left in the basket, how many muffins were in the basket when Goldilocks first put them on the porch?

So, if Papa Bear ate exactly 1/4 of the total, he ate 3 brownies. This leaves 9 brownies. Mama Bear eats exactly 1/3 of the remaining 9, so Mama Bear also ate 3 brownies leaving 6 brownies. Baby bear ate exactly 1/3 of the 6 remaining brownies, so Baby Bear also at 3 brownies.

Another way to look at the problem is with a 1 X 12 array, and then divide the array into 4 equal parts.

Now remove or color in the parts of the whole that each of the bears eats. Papa Bear ate 1/4 of the whole or all of the "A" brownies leaving the following:

Mama Bear ate 1/3 of the remaining brownies or all of the "B" brownies which leaves the following:

Now Baby Bear eats 1/2 of the remaining brownies or 1/2 which means he ate the "C" brownies. This leaves the "D" brownies for Goldilocks and the bears have their revenge!

Coin Puzzler

Puzzler: Kelly has 12 coins in her pocket. One-third of the coins are dimes. She has twice as many dimes as nickels. The rest of the coins are pennies. How much money does Kelly have in her pocket?

There are half as many nickels as dimes. This means there must be two nickels which equal $0.10. The rest of the coins are pennies. Since we have 6 coins so far (4 dimes + 2 nickels), we now know there are 6 pennies which equal $0.06. By adding up the totals for each set of coins ($0.40 + $0.10 +$0.06) we get an answer of $0.56.

Square Puzzler

Puzzler Click on this link for PDF.

Solution Click on this link for PDF.