Adding numbers is commutative. A launch that can stop halfway through a route is a different problem. Predict where it stops before you choose the path.
Every beast here has a target of ten. Below ten: feed it and stop. Exactly ten: clear it and stop. Above ten: clear it and carry the remainder to the next beast.
5The starting number One launch, target ten
ROUTE A
2 → 8
ROUTE B
8 → 2
Choose a prediction. You can compare all the steps afterward.
Trace A
Trace B
Original web exercises using a simplified target-ten rule. These are not app levels or screenshots. There is no aiming, physics, board geometry or progression here, and no claim that either route is physically reachable on an app board.
Paper puzzle pack · two pages
Make the prediction away from the screen.
Six comparisons, space for a prediction and clear counts, and a separate answer key. Print page 1 for each player; keep page 2 aside until everyone has traced both routes. The PDF uses US Letter paper and can be printed with “fit to page” on A4.
No account or app needed. Original exercises by Honest Little Apps. These simplified routes are not levels taken from the app. Classroom and home printing are welcome.
Read all six paper puzzles
Launch 5. A: 2 → 8. B: 8 → 2. Predict A, B or a tie in the number cleared.
Launch 7. A: 5 → 8. B: 8 → 5. Predict A, B or a tie in the number cleared.
Launch 8. A: 4 → 9 → 7. B: 4 → 7 → 9. Predict A, B or a tie in the number cleared.
Launch 4. A: 3 → 7 → 9. B: 9 → 7 → 3. Predict A, B or a tie in the number cleared.
Launch 9. A: 1 → 6. B: 6 → 1. Predict A, B or a tie in the number cleared.
Launch 3. A: 9 → 8 → 4. B: 4 → 8 → 9. Predict A, B or a tie in the number cleared.
Open the complete answer key
Challenge 1: B clears more. A clears 0, B clears 1. A: 5 + 2 = 7: feed, stop. B: 5 + 8 = 13: clear, carry 3. 3 + 2 = 5: feed, stop.
Challenge 6: A clears more. A clears 2, B clears 0. A: 3 + 9 = 12: clear, carry 2. 2 + 8 = 10: clear, stop. B: 3 + 4 = 7: feed, stop.
For challenge 5, A leaves the 6 untouched. B changes the remaining 1 into a 6. Both clear one beast. Clear counts alone cannot identify a best complete-board move.
Compare the first collision.
A total across the whole route can hide an early stop. In the first challenge, both routes contain 2 and 8, but starting with 2 feeds the first beast. Starting with 8 clears one and sends a smaller number onward. Write the incoming number beside each target, not just the total at the end.
After a clear, the next calculation starts with the remainder. Do not reuse the original launch number. A 5 that hits an 8 leaves 3, so the following calculation uses 3.
A tie can still leave different work.
Challenge five deliberately ties on the number cleared. One route uses the launch exactly; the other feeds a remaining beast. A count alone does not describe the whole board afterward.
This lab asks only which route clears more in one launch. It does not calculate the fewest launches to solve a complete board, award stars or prove a globally best move. In a full puzzle, the remaining beasts and available shots matter too.
A three-question planning habit
Will the first hit stop the launch? Check below, equal to or above the target.
What number reaches the next beast? Carry only the amount above ten.
What remains afterward? Note untouched beasts, fed beasts and unused carry before calling a route better.
Try a challenge without revealing the steps. Say your prediction aloud, then compare each line. If the answer differs, find the first calculation where your trace diverged. You can retry without a timer, score or streak.
Why does order matter if addition is commutative?
The sum of all the numbers does not change. The process may end before all of them are used. Stopping rules make the intermediate sums important.
Does the bigger first target always win?
No. The six comparisons include ties, and a clear-count win is not necessarily the best complete-board plan. Follow the actual rule at each collision rather than replacing it with a shortcut.
Take the plan onto a board
Numbers become the projectiles.
Number Beasts: Bond Lab combines number bonds with turn-based aiming. Its listing describes 45 solver-checked stages, an on-device Daily Lab and a Workshop for building puzzles. Later boards add obstacles and rules that this simplified lab does not model.
Listed free, with no in-app purchases, ads or accounts. iPhone and iPad · iOS 18 or later. Check the current storefront for availability. This publisher-created companion is not an independent review or a claim of measured learning gains.