Rainbow Piggy Bank

A colorful, kid‑friendly explainer & calculator for a number pattern trick: keep adding 6 cents until the last three digits of your balance (in cents) show 666. This is a math puzzle — use it only with your own money and always follow grown‑up rules.

How it works — for smart kids

Goal: We want the balance’s last three cents digits to be …666. We look at the balance in cents (no decimals) and only care about the last three digits. That’s called mod 1000.

Every time we add 6 cents, the last three digits jump by 6. After a while, the pattern may land on 666 — or it might miss it forever. The rule is simple:

  • If target = (666 − (balance % 1000)) % 1000 is even → you can do it.
  • If that target is odd → it’s impossible using only 6‑cent steps.

Why? Because 6 and 1000 share a factor of 2. To hit exactly 666, the difference needs to be even. (Grown‑up name: solving a modular congruence.)

Safety & kindness: Only practice with your own pocket‑money account or a pretend account. Real banks have rules about tiny, repeated payments. Always ask a parent/guardian before doing money experiments.

Try the calculator
Use dot as decimal separator (e.g., 16.66). We’ll do the cents math safely.
Balance in cents
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Last three digits (mod 1000)
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Target to reach 666
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Possible?
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Number of 6¢ steps
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Total to send
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Final balance
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Explanation
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Tip for teachers/parents: Ask kids to predict “possible or not?” by checking if the target is even. Then reveal the answer and compare!
Mini‑lessons
  1. Count in steps: Adding 6 over and over is like skip‑counting: 0, 6, 12, 18…
  2. Look at the last three digits: Only the last three digits matter (that’s mod 1000), because adding 1000 cents doesn’t change them.
  3. Even‑odd secret: To land exactly on 666, the difference must be even. If it’s odd, you’ll hop over it forever.
  4. Fast path (grown‑up trick): If it’s possible, the smallest number of steps is n ≡ 167 × (target/2) (mod 500).
Friendly rules
  • Practice with pretend money or your own account only. Ask a grown‑up first.
  • Some banks charge fees or block tiny repeated payments. This page is for math fun and learning.
  • Be kind with money: never pester people with surprise transfers.