At this point we re-design the cards and holders. Instead of a patterned back to the cards we have the negative of the number. One side of a holder also shows the negative of the other.
So flipping
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJ9izScj-NwUhbZtc1reGigBtblEaDVOgejHDVKM3smMaUFXyZ6Li11wIPbfPv6dBiH8TaitpnAQ9-ZztsbRF9RyRHRc9-GpBnCaReitdZr6af3YYmEbDB8ydvwoOpPAd0C5kVUZBmldLP/s1600/image289.png)
gives
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgl5WvCXOxlMcoqenhr373f47jsqnJdAlxsRoekCQxTQ0zMLVsTCLX12TO8eJ74ScIQFfmlideRvk6DAyxCP91U8nSKOUvbRiQaorxQ6hO8KWT0t9GmTXUYyE6ttoioUWsm4qB04XjAj6BH/s1600/image291.png)
and vice versa.
Flipping
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSyDW7yxf-yk8Y_5yaN0Ymz_0KoPVZ4N-F0o3AWQ2PG_zJ_XvMSskGv3Z-JR-sBKvp3ViFAjGKF9MjjsmmR_q9H8jxiCUHBgcws7nkLN6zCezXQOmRu5Eo1wVxX468e5CPZ5YnXJsY7snZ/s1600/image293.png)
gives
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgAk8BkyXpoxYd6AMbq2HXTahzA_spykOkB-BXpq84NJL33YBNv3oWMWM2LvhWk2RRW_09OFRCO57zGTK1cgCXdgmAVZ1pVCGhB9HqxUUBy4ZEjRgNUkuGVwAnFuEtGolvZWLDtfHKqJOaC/s1600/image295.png)
and vice versa.
Flipping over
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgS9glawHoy3HkE9qDayi-Hyi6lHKoBhnjLuCcRo1LWPBrLXKlPBgPC5PW2VQIjz2C62yoWK7-xLx2PdfVpn-UO8f1lZqFXbhlWameMimG30xQPE8ilbr1k8cgUjtl-G2X3SmJlTjDPsjib/s1600/image297.png)
gives
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_wnaSU_ZfgONJhqC4T8MALLKn_yeLXNf6F_NGqc1MEOCtJgVbMYjfBlcKZ4Z2tDwhjoSykKveNuU366lhhLmtI_XyPKyE6bzFl-Cf6IpS5MEMxIzr_LKxICIchcKQan9AlrAHUgCpRNlB/s1600/image299.png)
and vice versa.
New Rule
(Not so new really as the rule has always been – instead of removing cards add their negative, now we are just applying this in bulk.)
Whenever there is a negative holder flip the holder and the cards.
Now when you have the hand
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOm1cfTYfW0noqlMokECXiBIZ7JhfbsKu2h11MunemPfUERJQihxMoRRlj9ImucojWVobhCxdQjONKKIw4wUnCTr-8PmVM1xQybmH0jchPYYOpV9vj8crDCgr4KVgy8uivpSzSXV2f3JL2/s1600/image301.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg40gI983i3mhiJBaFN1s_jMRrS-oxPQT9cqLVSJx-rWG6cK3comen5S4F4RD2NDK6H_HXkcxciqUooUCP56TFQ3SUZdk82yiwPL5rHY06PQ0EvSvVzkCiJojOwBFzTYSNknS3I9QmIAUcL/s1600/image303.png)
flip the negative holder to give
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOm1cfTYfW0noqlMokECXiBIZ7JhfbsKu2h11MunemPfUERJQihxMoRRlj9ImucojWVobhCxdQjONKKIw4wUnCTr-8PmVM1xQybmH0jchPYYOpV9vj8crDCgr4KVgy8uivpSzSXV2f3JL2/s1600/image301.png)
In summary
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhg89M-fpTBRf8lPM79EFljbLnIPfdzwLMytUJ3Ew9uliww4ytdLHktSCEMpA7XXa-BI7Du2asfUpIkZsdAirBzdfWlLzRwdPOKN7aXlXgeysvjA6mN0cR1Odl21hERaFM_cCUxEKXBciZq/s1600/image308.png)
and
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNVC58DHtMwGh_WaVxzj6c7ma9eLfbPhUR9GRkZ9m4ZPZPRJgt-vUFGv1ia0Qpbun-aKjuwH8vUfmolvNOCtx32AI6cv5l5M1mCEWfHSGrOD_vTH1i2GI53zEiLEDOPzr3hgCaQEPx9iy2/s1600/image310.png)
give the same result of twenty black counters, the number Twenty.
Recording 5 x 4 = (-5) x (-4) = 20
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVEnurum-89Ay2aJ_QV88VVBpskhrtoTRFDR013yUEzHrH01ItbJ1nD-YQkiXjmf5GRUV9TyxPLFP8Va6PRHi8p3KMJVVbTvIbSb0QWbHXCdv8qlvSUIekLqK4i_DV6gd3mQNV6WGBOZCS/s1600/image306.png)
and
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg40gI983i3mhiJBaFN1s_jMRrS-oxPQT9cqLVSJx-rWG6cK3comen5S4F4RD2NDK6H_HXkcxciqUooUCP56TFQ3SUZdk82yiwPL5rHY06PQ0EvSvVzkCiJojOwBFzTYSNknS3I9QmIAUcL/s1600/image303.png)
give the same result of twenty white counters, the number Negative Twenty.
Recording 5 x (-4) = (-5) x 4 = (-20).
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