Place numbers on a triangle, a square or a 3 by 3 grid so every side adds to the same total. Five levels, one answer each, with a printable worksheet.
A magic shape is a drawing with circles on it, and a rule: every number is used once, and every line of the shape adds up to the same total. On a triangle with six circles, each side holds three circles and the sides share the corners. On a square with eight circles, each side holds three circles and the corners are shared again. On a 3 by 3 grid with nine cells, every row, every column and both long diagonals add to the same number. The skill is guess and check with a plan. A child learns to look at the circles that sit on two lines at once, to add three small numbers in their head, and to change one guess when a total is wrong. It also trains working backwards: if a side must reach 10 and two numbers are known, the third is what is left over.
Level 1, Almost done, is a triangle with the numbers 1 to 6 where one or two circles are empty and the side total is printed. Level 2, Magic triangle, leaves three or four circles empty and still prints the total. Level 3, Secret total, hides the total as well: the question only says that all the sides add to the same number, and the child has to find which total is possible. Level 4, Magic square, uses the numbers 1 to 8 on a square, with four or five circles empty and the total shown. Level 5, Magic grid, is the 3 by 3 grid with the numbers 1 to 9 and the total 15 shown, with five or six cells empty. All the numbers in a puzzle are used exactly once. The number tiles also contain a couple of numbers that are not in the puzzle at all, such as 0 or 10, so a wrong tile can never be right by luck.
The game lists every way to place the numbers on each shape before it starts. There are 24 ways on the triangle, with totals of 9, 10, 11 and 12, 48 ways on the square and 8 ways on the 3 by 3 grid, which are the well-known magic squares with a total of 15 and the 5 in the centre. To make a puzzle it picks one of those ways, hides some circles, and counts how many of the listed ways still match what is shown, including the printed total when there is one. It keeps the puzzle only when the count is exactly 1. So each puzzle has one answer. The check button is slightly more general than that: it accepts any filling that follows the rules, and because only one filling exists, that is the same answer. The tests repeat the count with a separate search for 500 puzzles on every level.
A worksheet holds 4, 6 or 8 new shapes at the level you pick, on Letter or A4 paper, with big circles to write in and an answer key on the last page. The PDF is made in your browser and nothing is uploaded. The game has no timer, takes no points away for a wrong try, and has no ads in the play area. Because the shapes are small, the set of puzzles is limited: the 3 by 3 grid has only 8 solutions, so on level 5 you will see familiar patterns turned and flipped. That is part of the lesson, since the same grid can be rotated and mirrored. This page does not teach multiplication or fractions. It practises addition of three small numbers, with totals from 9 to 15, and it works best when an adult sits beside a 6 or 7 year old on levels 3 to 5.
A triangle with six circles, one at each corner and one in the middle of each side. You place 1 to 6 once each so the three circles on every side add to the same total, which can only be 9, 10, 11 or 12.
Yes. The game lists every possible arrangement of the shape and keeps a puzzle only when exactly one arrangement fits the numbers and total shown. The check button accepts any correct arrangement, which is the same one.
The numbers 1 to 9 add to 45. Three rows share that 45 equally, so each row is 45 divided by 3, which is 15. The middle number is always 5.
Ages 6 to 8. A first-grader can finish level 1 with one empty circle. Levels 3 to 5 need patient guess and check and suit a strong 7 or 8 year old.
They are decoys. The puzzle only uses its own numbers once each, so a decoy can never be right. They make your child think about which numbers are still unused.
Yes. Choose a level, 4, 6 or 8 shapes and Letter or A4. The PDF is built on your device, each print is new, and the answers are on the last page.