Target

You are given six numbers and a target from 100 to 999. Combine the numbers two at a time with +, −, × and ÷ until one of them is the target.

Combining two numbers replaces them with their result. Every result must be a positive whole number: you cannot subtract a number from one that is not larger, nor divide where there would be a remainder. Each number is used at most once, and you need not use them all.

Every target can be made exactly.

Controls

On a touch screen, a tap does what a click does.

Click a number or operator to pick it: a number, then an operator, then another number combines the two numbers.

With the keyboard, the arrow keys move a cursor around the board. Enter or Space does what a click does to the number or operator under it.

The smaller number slides onto the larger, and the result takes the larger’s place and says how it was made beneath its value. Which of the two you pick first makes no difference: − and ÷ always take the smaller number from or into the larger. Once a number and an operator are picked, the numbers they cannot combine with are grayed out.

You can also pick an operator with its key: +, −, * (or x) and /. With no number picked, the key picks the number under the cursor as well, so from the keyboard a move is a number, an operator’s key and Enter on the second number. Escape puts down the number you picked. Undo takes back a combination.

Where the puzzle comes from

This is the numbers round of the British television quiz Countdown, where the six numbers are drawn from cards: two each of 1 to 10, and one each of 25, 50, 75 and 100.

Hints

Hint gives you one combination and no more: how few operations you can still finish in from the numbers you have now, how many different combinations start a way that short, and one of them, starting with the work on the biggest number. “You can finish in 5 more operations, starting 4 ways. One of them: 100 + 3 = 103.” Where only one combination starts a way that short, the hint says so. The rest of the way is yours to find, and the next hint picks up from wherever you are.

If the numbers you have left can no longer make the target, the hint says so, and Undo takes you back to where they could.

Not in this game

Target parameters

These parameters are available from the ‘Custom type…’ option on the ‘Type’ menu.

Large numbers
How many of the six numbers are drawn from the large ones, 25, 50, 75 and 100; the rest are drawn from two each of 1 to 10. It must be between 0 and 4.
Difficulty
Determine the difficulty of the generated puzzle; see what the names mean.

The tier is the fewest operations that make the target: two at Easy, three at Normal, four at Tricky and five at Hard.

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