Enigma 1147: Multiply and add
3 October 2016
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From New Scientist #2303, 11th August 2001 [link]
Matthew is practising his multiplication and addition. He had a board (as below) and nine cards labelled 1,2,3,…,8,9.
He shuffles the cards and deals them on to the board, one to each square. For each square, he multiplies the number on the board by the number on the card in that square. Finally he adds together the nine products he has obtained to give his final number.
When I watched Matthew play the game his final number was 545. When he had finished he then moved some of the cards. Each card he moved went one square horizontally or vertically, but not diagonally, to another square on the board. I can’t remember all the cards he moved, but I do know he moved the cards in the four corner squares. He then had a new layout with one card in each square and he repeated his multiply and add routine. When he told me his final number, I asked him how many factors it had. After a while he told me he had found 20 but had still not finished his search.
What was Matthew’s final number after he had moved the cards?