"O, Mr Squirrel, do," she said again.
He offered her a third nut, and then he whistled shrilly; it sounded more like a baby crying than a whistle. Then to her surprise, as she looked down the wood path, Hansi saw a troop of little men, such as you see on Christmas cards in Germany, with red caps and green jackets and wooden shoes turned up at the toes. "Real Heinzelmen and no mistake," thought Hansi delightedly, "they can help me, if anyone can." She counted them, they were seven in number, like Snowdrop's dwarfs. They made quite a noise as they marched up in order, whistling a merry tune. When they saw Hansi, they took off their red caps, and their white hair flew about them like a mist, till Hansi could hardly see them any more. The squirrel screamed and shouted at them, and they answered him; but Hansi could not understand at first what it was all about. She thought they must be talking English; she knew a lady who lived near them, and who could only talk English, poor thing. All of a sudden the earth trembled—was it an earthquake? Hansi held tight on to the fir-tree, though its needles hurt her hands. All she saw was the seven little men disappearing into the ground down a long slide such as firemen use, when they are called suddenly from sleep, and are carried by a new mechanical apparatus direct from one floor to the other. The earth closed up again, and Hansi thought it must be all a dream; but in two seconds they were back again with silver hatchets and silver pails. With the hatchets they immediately began to hack away at the tree. They made tremendous efforts, and became quite red in the face. The last moment before it was finally felled, the squirrel bounded off, and tossed a nut to Hansi, who caught it cleverly in her pinafore.
"Dear little men," she said, "may I have the tree? Will you bring it home for me, and I will give you all my Christmas cake? But I have nothing to hang on it, and make it pretty," she continued. The dwarfs began to chatter again like so many girls, all trying to say the same thing at once. Then they marched along, dragging the tree with them.
"O, Mr Dwarf, that's the wrong way home, I'm sure," said Hansi. But she followed them all the same. They came to where a crystal stream leapt over a little group of rocks. The dwarfs held their buckets under the cascade, and caught some drops. The drops turned into silver fish, each with a little loop on the end of its tail, all ready to hang on the tree.
They then took Hansi's pine cones and ferns and grasses, and even collected the frozen cobwebs from the bushes and let the spray from the waters fall on them, and lo and behold the most exquisite gems were ready for the decoration of the Christmas tree.
"You live at No 7, and you are seven years old," said the eldest of the dwarfs, addressing Hansi. ("However could he have known that?" she thought.) "Perhaps you can tell me what seven times seven makes?"
Hansi considered a moment. "No, we have not got so far as that in our arithmetic," she replied. "Twice seven is fourteen, that I know."
"Seven times seven is forty-nine and is the square of seven," said the dwarf. "Always remember that, for it is a most important fact in magic!"
Rummaging in his pocket, he took out a note-book and handed a leaf to her with this diagram and inscription on it