(harder version)

Winter has settled in to stay where I live and the last time Barney, Danny and Gina stayed with me, we decided to build a fire in the fireplace. The children and I settled down to read, but the warmth of the fire made me sleepy and I must have dozed off a minute, when I awoke suddenly to see Danny and Gina parading into the family room with bath towels wrapped around their heads like turbans. “I am the Swami Llami !” declared Danny adjusting his towel turban on his head. “I know all. I see all. I have special powers!” “And I am his helper, the great Gina Lola Reada – you- Minda!” giggled Gina. “I knew this peace and quiet couldn’t last,” groaned Barney, putting aside his book. “What are you two up to?”

“Watch and be amazed!” answered Danny, dramatically. I watched with amusement as Danny took the 2 large dice that we often used for games from under his turban. Stopping only a minute to fix his towel again, he said, “I can toss these dice on the floor near this magic fire, and my assistant can tell you the sum of the numbers!”

“Seeing is believing!” replied Barney. “Show me how you do that, Gina!” Barney’s tone told me he didn’t think Gina, who is in kindergarten, was quite old enough to do this addition, but he would be impressed if she did. Danny tossed the two dice onto the carpet near the hearth. The number 3 and 2 came up. Gina used her fingers to help her and proudly announced “5! The Great Gina Lola Reada- You - Minda says 5! That was an easy one!” “Cool!” said Barney. “That’s pretty good adding for a 5 year old, but it’s not really magic or mind reading. You used your fingers to figure it out, didn’t you?”

“Remember, oh unbelieving one,” said Danny. “Gina is only my assistant. She has much to learn from the great Swami Llami! I, on the other hand, can do greater feats.”

Danny then took 5 dice out from under his towel “turban” and, with his eyes closed, stacked them one on top of the other. He then opened his eyes, and, without touching the dice, quickly told Barney the sum of the sides that were hidden from view! Barney checked by picking up the dice, and sure enough, Danny’s sum had been correct! “Impossible!” snorted Barney. “There’s no way you could know that! That was just luck. You can’t do it again,” said Barney confidently. “I wouldn’t be too sure about that,” I advised. “Danny, close your eyes and we will roll them again and stack them while you are not looking. Barney rolled the dice again and stacked the 5 dice. (The number 4 was on top.) “Oh, Great Swami Llami, what is the total of the numbers we cannot see?”
Holding both hands near his temples and rubbing slowly, Danny said, “My mystical powers tell me that the total of the numbers hidden from Barney’s sight is …31!” “How did he do that, Aunt Mathilda?” Barney asked after turning over the dice to find that Danny was correct again!
How did Danny do it? Was it just luck? Was he using trick dice? Can he do magic? Write to me and let me know what you think. Post your thinking on the solution board and I will get back to you soon. I want to hear what you think about this! (You might want to try it a few times yourself and see if you can figure out what he did.) When you think you have the correct solution, be sure to show a teacher, parent or friend your work and explain your method to them. Then, if they agree that your answer makes sense, post it on the message board. I am especially interested to hear what strategy you used to figure out the answer, and whether you did it with a friend, parent, or by yourself. Be sure to include your first name or email nick name only, your teacher’s name, school and email address. If you do, I will answer you soon on the message board! (You could also send me some diet tips!)

Love,
Aunty Math

P.S.
If you know how Danny did this amazing feat, don’t be too quick to share it with your friends. Perhaps they may be able to figure it out themselves, which would be much more valuable than your telling them. Be a friend and let them think about it a while!

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